## Essentials of Statistics Study Set 1

Statistics

## Quiz 9 :

Hypothesis Tests

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Q55 Q55 Q55

The average hourly wage of computer programmers with 2 years of experience has been $21.80. Because of high demand for computer programmers, it is believed there has been a significant increase in the average wage of computer programmers. To test whether or not there has been an increase, the correct hypotheses to be tested are

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Q57 Q57 Q57

In the past, 75% of the tourists who visited Chattanooga went to see Rock City. The management of Rock City recently undertook an extensive promotional campaign. They are interested in determining whether the promotional campaign actually increased the proportion of tourists visiting Rock City. The correct set of hypotheses is

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Q58 Q58 Q58

The average life expectancy of tires produced by the Whitney Tire Company has been 40,000 miles. Management believes that due to a new production process, the life expectancy of their tires has increased. In order to test the validity of their belief, the correct set of hypotheses is

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Multiple Choice

Q59 Q59 Q59

A soft drink filling machine, when in perfect adjustment, fills the bottles with 12 ounces of soft drink. Any over filling or under filling results in the shutdown and readjustment of the machine. To determine whether or not the machine is properly adjusted, the correct set of hypotheses is

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Multiple Choice

Q74 Q74 Q74

Exhibit 9-4
The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in the sample to check out was 3.1 minutes with a standard deviation of 0.5 minutes. We want to test to determine whether or not the mean waiting time of all customers is significantly more than 3 minutes.
-Refer to Exhibit 9-4. The test statistic is

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Q75 Q75 Q75

Exhibit 9-4
The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in the sample to check out was 3.1 minutes with a standard deviation of 0.5 minutes. We want to test to determine whether or not the mean waiting time of all customers is significantly more than 3 minutes.
-Refer to Exhibit 9-4. The p-value is between

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Multiple Choice

Q76 Q76 Q76

Exhibit 9-4
The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in the sample to check out was 3.1 minutes with a standard deviation of 0.5 minutes. We want to test to determine whether or not the mean waiting time of all customers is significantly more than 3 minutes.
-Refer to Exhibit 9-4. At 95% confidence, it can be concluded that the mean of the population is

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Multiple Choice

Q77 Q77 Q77

Exhibit 9-5
A random sample of 100 people was taken. Eighty-five of the people in the sample favored Candidate A. We are interested in determining whether or not the proportion of the population in favor of Candidate A is significantly more than 80%.
-Refer to Exhibit 9-5. The test statistic is

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Q78 Q78 Q78

Exhibit 9-5
A random sample of 100 people was taken. Eighty-five of the people in the sample favored Candidate A. We are interested in determining whether or not the proportion of the population in favor of Candidate A is significantly more than 80%.
-Refer to Exhibit 9-5. The p-value is

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Q79 Q79 Q79

Exhibit 9-5
A random sample of 100 people was taken. Eighty-five of the people in the sample favored Candidate A. We are interested in determining whether or not the proportion of the population in favor of Candidate A is significantly more than 80%.
-Refer to Exhibit 9-5. At 95% confidence, it can be concluded that the proportion of the population in favor of candidate A

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Multiple Choice

Q80 Q80 Q80

Exhibit 9-6
A random sample of 16 students selected from the student body of a large university had an average age of 25 years and a standard deviation of 2 years. We want to determine if the average age of all the students at the university is significantly more than 24. Assume the distribution of the population of ages is normal.
-Refer to Exhibit 9-6. The test statistic is

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Multiple Choice

Q81 Q81 Q81

Exhibit 9-6
A random sample of 16 students selected from the student body of a large university had an average age of 25 years and a standard deviation of 2 years. We want to determine if the average age of all the students at the university is significantly more than 24. Assume the distribution of the population of ages is normal.
-Refer to Exhibit 9-6. The p-value is between

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Multiple Choice

Q82 Q82 Q82

Exhibit 9-6
A random sample of 16 students selected from the student body of a large university had an average age of 25 years and a standard deviation of 2 years. We want to determine if the average age of all the students at the university is significantly more than 24. Assume the distribution of the population of ages is normal.
-Refer to Exhibit 9-6. At 95% confidence, it can be concluded that the mean age is

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Multiple Choice

Q83 Q83 Q83

Exhibit 9-7
A random sample of 16 statistics examinations from a large population was taken. The average score in the sample was 78.6 with a variance of 64. We are interested in determining whether the average grade of the population is significantly more than 75. Assume the distribution of the population of grades is normal.
-Refer to Exhibit 9-7. The test statistic is

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Multiple Choice

Q84 Q84 Q84

Exhibit 9-7
A random sample of 16 statistics examinations from a large population was taken. The average score in the sample was 78.6 with a variance of 64. We are interested in determining whether the average grade of the population is significantly more than 75. Assume the distribution of the population of grades is normal.
-Refer to Exhibit 9-7. The p-value is between

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Q85 Q85 Q85

Exhibit 9-7
A random sample of 16 statistics examinations from a large population was taken. The average score in the sample was 78.6 with a variance of 64. We are interested in determining whether the average grade of the population is significantly more than 75. Assume the distribution of the population of grades is normal.
-Refer to Exhibit 9-7. At 95% confidence, it can be concluded that the average grade of the population

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Multiple Choice

Q86 Q86 Q86

Exhibit 9-8
The average gasoline price of one of the major oil companies in Europe has been $1.25 per liter. Recently, the company has undertaken several efficiency measures in order to reduce prices. Management is interested in determining whether their efficiency measures have actually reduced prices. A random sample of 49 of their gas stations is selected and the average price is determined to be $1.20 per liter. Furthermore, assume that the standard deviation of the population σ) is $0.14.
-Refer to Exhibit 9-8. The standard error has a value of

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Multiple Choice

Q87 Q87 Q87

Exhibit 9-8
The average gasoline price of one of the major oil companies in Europe has been $1.25 per liter. Recently, the company has undertaken several efficiency measures in order to reduce prices. Management is interested in determining whether their efficiency measures have actually reduced prices. A random sample of 49 of their gas stations is selected and the average price is determined to be $1.20 per liter. Furthermore, assume that the standard deviation of the population σ) is $0.14.
-Refer to Exhibit 9-8. The value of the test statistic for this hypothesis test is

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Q88 Q88 Q88

Exhibit 9-8
The average gasoline price of one of the major oil companies in Europe has been $1.25 per liter. Recently, the company has undertaken several efficiency measures in order to reduce prices. Management is interested in determining whether their efficiency measures have actually reduced prices. A random sample of 49 of their gas stations is selected and the average price is determined to be $1.20 per liter. Furthermore, assume that the standard deviation of the population σ) is $0.14.
-Refer to Exhibit 9-8. The p-value for this problem is

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Multiple Choice

Q89 Q89 Q89

Exhibit 9-9
The sales of a grocery store had an average of $8,000 per day. The store introduced several advertising campaigns in order to increase sales. To determine whether or not the advertising campaigns have been effective in increasing sales, a sample of 64 days of sales was selected. It was found that the average was $8,300 per day.
From past information, it is known that the standard deviation of the population is $1,200.
-Refer to Exhibit 9-9. The correct null hypothesis for this problem is

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Q90 Q90 Q90

Exhibit 9-9
The sales of a grocery store had an average of $8,000 per day. The store introduced several advertising campaigns in order to increase sales. To determine whether or not the advertising campaigns have been effective in increasing sales, a sample of 64 days of sales was selected. It was found that the average was $8,300 per day.
From past information, it is known that the standard deviation of the population is $1,200.
-Refer to Exhibit 9-9. The value of the test statistic is

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Multiple Choice

Q91 Q91 Q91

Exhibit 9-9
The sales of a grocery store had an average of $8,000 per day. The store introduced several advertising campaigns in order to increase sales. To determine whether or not the advertising campaigns have been effective in increasing sales, a sample of 64 days of sales was selected. It was found that the average was $8,300 per day.
From past information, it is known that the standard deviation of the population is $1,200.
-Refer to Exhibit 9-9. The p-value is

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Multiple Choice

Q92 Q92 Q92

The Department of Economic and Community Development DECD) reported that in 2009 the average number of new jobs created per county was 450. The department also provided the following information regarding a sample of 5 counties in 2010.
County New Jobs Created In 2010
Bradley 410
Rhea 480
Marion 407
Grundy 428
Sequatchie 400
a. Compute the sample average and the standard deviation for 2010.
b. We want to determine whether there has been a significant decrease in the average number of jobs created. Provide the null and the alternative hypotheses.
c. Compute the test statistic.
d. Compute the p-value; and at 95% confidence, test the hypotheses. Assume the population is normally distributed.

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Q93 Q93 Q93

The Bureau of Labor Statistics reported that the average yearly income of dentists in the year 2009 was $110,000. A sample of 81 dentists, which was taken in 2010, showed an average yearly income of $120,000. Assume the standard deviation of the population of dentists in 2010 is $36,000.
a. We want to test to determine if there has been a significant increase in the average yearly income of dentists. Provide the null and the alternative hypotheses.
b. Compute the test statistic.
c. Determine the p-value; and at 95% confidence, test the hypotheses.

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Q94 Q94 Q94

A producer of various kinds of batteries has been producing "D" size batteries with a life expectancy of 87 hours. Due to an improved production process, management believes that there has been an increase in the life expectancy of their "D" size batteries. A sample of 36 batteries showed an average life of 88.5 hours. Assume from past information that it is known that the standard deviation of the population is 9 hours.
a. Give the null and the alternative hypotheses.
b. Compute the test statistic.
c. At 99% confidence using the critical value approach, test management's belief.
d. What is the p-value associated with the sample results? What is your conclusion based on the
p-value?

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Q95 Q95 Q95

Choo Choo Paper Company makes various types of paper products. One of their products is a 30 mils thick paper. In order to ensure that the thickness of the paper meets the 30 mils specification, random cuts of paper are selected and the thickness of each cut is measured. A sample of 256 cuts had a mean thickness of 30.3 mils with a standard deviation of 4 mils.
a. Compute the standard error of the mean.
b.
b. At 95% confidence using the critical value approach, test to see if the mean thickness is significantly more than 30 mils.
c. Show that the p-value approach results in the same conclusion as that of part

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Q96 Q96 Q96

Last year, 50% of MNM, Inc. employees were female. It is believed that there has been a reduction in the percentage of females in the company. This year, in a random sample of 400 employees, 180 were female.
a. Give the null and the alternative hypotheses.
b.
b. At 95% confidence using the critical value approach, determine if there has been a significant reduction in the proportion of females.
c. Show that the p-value approach results in the same conclusion as that of Part

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Q97 Q97 Q97

Last year, a soft drink manufacturer had 21% of the market. In order to increase their portion of the market, the manufacturer has introduced a new flavor in their soft drinks. A sample of 400 individuals participated in the taste test and 100 indicated that they like the taste. We are interested in determining if more than 21% of the population will like the new soft drink.
a. Set up the null and the alternative hypotheses.
b. Determine the test statistic.
c. Determine the p-value.
d. At 95% confidence, test to determine if more than 21% of the population will like the new soft drink.

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Q98 Q98 Q98

In the past, the average age of employees of a large corporation has been 40 years. Recently, the company has been hiring older individuals. In order to determine whether there has been an increase in the average age of all the employees, a sample of 64 employees was selected. The average age in the sample was 45 years with a standard deviation of 16 years. Let α = .05.
a. State the null and the alternative hypotheses.
b. Compute the test statistic.
c. Using the p-value approach, test to determine whether or not the mean age of all employees is significantly more than 40 years.

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Q99 Q99 Q99

The average gasoline price of one of the major oil companies has been $2.20 per gallon. Because of cost reduction measures, it is believed that there has been a significant reduction in the average price. In order to test this belief, we randomly selected a sample of 36 of the company's gas stations and determined that the average price for the stations in the sample was $2.14. Assume that the standard deviation of the population σ) is $0.12.
a. State the null and the alternative hypotheses.
b. Compute the test statistic.
c. What is the p-value associated with the above sample results?
d. At 95% confidence, test the company's claim.

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Q100 Q100 Q100

A sample of 81 account balances of a credit company showed an average balance of $1,200 with a standard deviation of $126.
a. Formulate the hypotheses that can be used to determine whether the mean of all account balances is significantly different from $1,150.
b. Compute the test statistic.
c. Using the p-value approach, what is your conclusion? Let α = .05.

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Q101 Q101 Q101

From a population of cans of coffee marked "12 ounces," a sample of 50 cans was selected and the contents of each can were weighed. The sample revealed a mean of 11.8 ounces with a standard deviation of 0.5 ounces.
a. Formulate the hypotheses to test to see if the mean of the population is at least 12 ounces.
b. Compute the test statistic.
c. Using the p-value approach, what is your conclusion? Let α = .05.

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Q102 Q102 Q102

A lathe is set to cut bars of steel into lengths of 6 centimeters. The lathe is considered to be in perfect adjustment if the average length of the bars it cuts is 6 centimeters. A sample of 121 bars is selected randomly and measured. It is determined that the average length of the bars in the sample is 6.08 centimeters with a standard deviation of 0.44 centimeters.
a. Formulate the hypotheses to determine whether or not the lathe is in perfect adjustment.
b. Compute the test statistic.
c. Using the p-value approach, what is your conclusion? Let α = .05.

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Q103 Q103 Q103

Ahmadi, Inc. has been manufacturing small automobiles that have averaged 50 miles per gallon of gasoline in highway driving. The company has developed a more efficient engine for its small cars and now advertises that its new small cars average more than 50 miles per gallon in highway driving. An independent testing service road- tested 64 of the automobiles. The sample showed an average of 51.5 miles per gallon with a standard deviation of 4 miles per gallon.
a. Formulate the hypotheses to determine whether or not the manufacturer's advertising campaign is legitimate.
b. Compute the test statistic.
c. What is the p-value associated with the sample results and what is your conclusion? Let α =
.05.

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Q104 Q104 Q104

A soft drink filling machine, when in perfect adjustment, fills the bottles with 12 ounces of soft drink. A random sample of 49 bottles is selected, and the contents are measured. The sample yielded a mean content of 11.88 ounces with a standard deviation of 0.35 ounces.
a. Formulate the hypotheses to test to determine if the machine is in perfect adjustment.
b. Compute the value of the test statistic.
c. Compute the p-value and give your conclusion regarding the adjustment of the machine. Let α =
.05.

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Q105 Q105 Q105

"D" size batteries produced by MNM Corporation have had a life expectancy of 87 hours. Because of an improved production process, it is believed that there has been an increase in the life expectancy of its "D" size batteries. A sample of 36 batteries showed an average life of 88.5 hours. Assume from past information that it is known that the standard deviation of the population is 9 hours.
a. Formulate the hypotheses for this problem.
b. Compute the test statistic.
c. What is the p-value associated with the sample results? What is your conclusion based on the p-value? Let α = .05.

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Q106 Q106 Q106

At a local university, a sample of 49 evening students was selected in order to determine whether the average age of the evening students is significantly different from 21. The average age of the students in the sample was 23 with a standard deviation of 3.5.
a. Formulate the hypotheses for this problem.
b. Compute the test statistic.
c. Determine the p-value and test these hypotheses. Let α = .05.

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Q107 Q107 Q107

In order to determine the average price of hotel rooms in Atlanta, a sample of 64 hotels was selected. It was determined that the average price of the rooms in the sample was $108.50 with a standard deviation of $16.
a. Formulate the hypotheses to determine whether or not the average room price is significantly different from $112.
b. Compute the test statistic.
c. At 95% confidence using the p-value approach, test the hypotheses. Let α = 0.1.

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Q108 Q108 Q108

Identify the null and alternative hypotheses for the following problems.
a. The manager of a restaurant believes that it takes a customer less than or equal to 25 minutes to eat lunch.
b. Economists have stated that the marginal propensity to consume is at least 90¢ out of every
dollar.
c. It has been stated that 75 out of every 100 people who go to the movies on Saturday night buy popcorn.

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Q109 Q109 Q109

A student believes that the average grade on the statistics final examination was 87. A sample of 36 final examinations was taken. The average grade in the sample was 83.96 with a standard deviation of 12.
a. State the null and alternative hypotheses.
b. Using the critical value approach, test the hypotheses at the 5% level of significance.
c. Using the p-value approach, test the hypotheses at the 5% level of significance.

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Q110 Q110 Q110

A carpet company advertises that it will deliver your carpet within 15 days of purchase. A sample of 49 past customers is taken. The average delivery time in the sample was 16.2 days. The standard deviation of the population σ) is known to be 5.6 days.
a. State the null and alternative hypotheses.
b. Using the critical value approach, test to determine if their advertisement is legitimate. Let α = .05.
c. Using the p-value approach, test the hypotheses at the 5% level of significance.

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Q111 Q111 Q111

A sample of 30 cookies is taken to test the claim that each cookie contains at least 9 chocolate chips. The average number of chocolate chips per cookie in the sample was 7.8 with a standard deviation of 3.
a. State the null and alternative hypotheses.
b. Using the critical value approach, test the hypotheses at the 5% level of significance.
c. Using the p-value approach, test the hypothesis at the 5% level of significance.
d. Compute the probability of a Type II error if the true number of chocolate chips per cookie is 8.

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Q112 Q112 Q112

A group of young businesswomen wish to open a high fashion boutique in a vacant store but only if the average income of households in the area is at least $25,000. A random sample of 9 households showed the following results.
Assume the population of incomes is normally distributed.
a. Compute the sample mean and the standard deviation.
b. State the hypotheses for this problem.
c. Compute the test statistic.
d. At 95% confidence using the p-value approach, what is your conclusion?

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Q113 Q113 Q113

Nancy believes that the average running time of movies is equal to 140 minutes. A sample of 4 movies was taken and the following running times were obtained. Assume the population of the running times is normally distributed.
150 150 180 170
a. Compute the sample mean and the standard deviation.
b. State the null and alternative hypotheses.
c. Using the critical value approach, test the hypotheses at the 10% level of significance.
d. Using the p-value approach, test the hypotheses at the 10% level of significance.

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Q114 Q114 Q114

A student believes that no more than 20% i.e., ≤ 20%) of the students who finish a statistics course get an A. A
random sample of 100 students was taken. Twenty-four percent of the students in the sample received A's.
a. State the null and alternative hypotheses.
b. Using the critical value approach, test the hypotheses at the 1% level of significance.
c. Using the p-value approach, test the hypotheses at the 1% level of significance.

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Q115 Q115 Q115

An official of a large national union claims that the fraction of women in the union is not significantly different from one-half. Using the critical value approach and the sample information reported below, carry out a test of this statement. Let α = 0.05.
sample size 400
women 168
men 232

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Q116 Q116 Q116

A law enforcement agent believes that at least 88% of the drivers stopped on Saturday nights for speeding are under the influence of alcohol. A sample of 66 drivers who were stopped for speeding on a Saturday night was taken. Eighty percent of the drivers in the sample were under the influence of alcohol.
a. State the null and alternative hypotheses.
b. Compute the test statistic.
c. Using the p-value approach, test the hypotheses at the .05 level of significance.

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Q117 Q117 Q117

Two thousand numbers are selected randomly; 960 were even numbers.
a. State the hypotheses to determine whether the proportion of odd numbers is significantly different from 50%.
b. Compute the test statistic.
c. At 90% confidence using the p-value approach, test the hypotheses.

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Q118 Q118 Q118

In the last presidential election, a national survey company claimed that no more than 50% i.e., ≤ 50%) of all registered voters voted for the Republican candidate. In a random sample of 400 registered voters, 208 voted for the Republican candidate.
a. State the null and the alternative hypotheses.
b. Compute the test statistic.
c. At 95% confidence, compute the p-value and test the hypotheses.

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Q119 Q119 Q119

An automobile manufacturer stated that it will be willing to mass produce electric-powered cars if more than 30% of potential buyers indicate they will purchase the newly designed electric cars. In a sample of 500 potential buyers, 160 indicated that they would buy such a product.
a. State the hypotheses for this problem
b. Compute the standard error of .
c. Compute the test statistic.
d. At 95% confidence, what is your conclusion? Should the manufacturer produce the new electric powered car?

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Q120 Q120 Q120

It is said that more males register to vote in a national election than females. A research organization selected a random sample of 300 registered voters and reported that 165 of the registered voters were male.
a. Formulate the hypotheses for this problem.
b. Compute the standard error of .
c. Compute the test statistic.
d. Using the p-value approach, can you conclude that more males registered to vote than females? Let α = .05.

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Q121 Q121 Q121

Consider the following hypothesis test:
Ho: μ = 10
Ha: μ ≠ 10
A sample of 81 provides a sample mean of 9.5 and a sample standard deviation of 1.8.
a. Determine the standard error of the mean.
b. Compute the value of the test statistic.
c. Determine the p-value; and at 95% confidence, test the above hypotheses.

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Q122 Q122 Q122

Consider the following hypothesis test:
Ho: μ ≥ 14
Ha: μ < 14
A sample of 64 provides a sample mean of 13 and a sample standard deviation of 4.
a. Determine the standard error of the mean.
b. Compute the value of the test statistic.
c. Determine the p-value; and at 95% confidence, test the above hypotheses.

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Q123 Q123 Q123

Consider the following hypothesis test:
Ho: μ ≥ 40
Ha: μ < 40
A sample of 49 provides a sample mean of 38 and a sample standard deviation of 7.
a. Determine the standard error of the mean.
b. Compute the value of the test statistic.
c. Determine the p-value; and at 95% confidence, test the above hypotheses.

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Q124 Q124 Q124

Consider the following hypothesis test:
Ho: P ≤ 0.8
Ha: P > 0.8
A sample of 400 provided a sample proportion of 0.853.
a. Determine the standard error of the proportion.
b. Compute the value of the test statistic.
c. Determine the p-value; and at 95% confidence, test the above hypotheses.

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Q125 Q125 Q125

You are given the following information obtained from a random sample of 5 observations. Assume the population has a normal distribution.
20 18 17 22 18
You want to determine whether or not the mean of the population from which this sample was taken is significantly less than 21.
a. State the null and the alternative hypotheses.
b. Compute the standard error of the mean.
c. Determine the test statistic.
d. Determine the p-value and at 90% confidence, test whether or not the mean of the population is significantly less than 21.

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Q126 Q126 Q126

Consider the following hypothesis test:
Ho: p = 0.5
Ha: p ≠ 0.5
A sample of 800 provided a sample proportion of 0.58.
a. Determine the standard error of the proportion.
b. Compute the value of the test statistic.
c. Determine the p-value, and at 95% confidence, test the hypotheses.

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Q127 Q127 Q127

You are given the following information obtained from a random sample of 4 observations. 25 47 32 56
You want to determine whether or not the mean of the population from which this sample was taken is significantly different from 48. Assume the population is normally distributed.)
a. State the null and the alternative hypotheses.
b. Determine the test statistic.
c. Determine the p-value; and at 95% confidence test to determine whether or not the mean of the population is significantly different from 48.

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Q128 Q128 Q128

Confirmed cases of West Nile virus in birds for a sample of six counties in the state of Georgia are shown below.
We are interested in testing the following hypotheses regarding these data: Ho: μ ≤ 3
Ha: μ > 3
a. Compute the mean and the standard deviation of the sample.
b. Compute the standard error of the mean.
c. Determine the test statistic.
d. Determine the p-value and at 95% confidence, test the hypotheses.

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Q129 Q129 Q129

A sample of 64 account balances from a credit company showed an average daily balance of $1,040. The standard deviation of the population is known to be $200. We are interested in determining if the mean of all account balances i.e., population mean) is significantly different from $1,000.
a. Develop the appropriate hypotheses for this problem.
b. Compute the test statistic.
c. Compute the p-value.
d. Using the p-value approach at 95% confidence, test the above hypotheses.
e. Using the critical value approach at 95% confidence, test the hypotheses.

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Q130 Q130 Q130

Consider the following hypotheses test.
Ho: μ ≥ 80 Ha: μ < 80
A sample of 121 provided a sample mean of 77.3. The population standard deviation is known to be 16.5.
a. Compute the value of the test statistic.
b. Determine the p-value; and at 93.7% confidence, test the above hypotheses.
c. Using the critical value approach at 93.7% confidence, test the hypotheses.

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Q131 Q131 Q131

Automobiles manufactured by the Efficiency Company have been averaging 42 miles per gallon of gasoline in highway driving. It is believed that its new automobiles average more than 42 miles per gallon. An independent testing service road-tested 36 of the automobiles. The sample showed an average of 42.8 miles per gallon with a standard deviation of 1.2 miles per gallon.
a. With a 0.05 level of significance using the critical value approach, test to determine whether or not the new automobiles actually do average more than 42 miles per gallon.
b. What is the p-value associated with the sample results? What is your conclusion based on the
p-value?

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Q132 Q132 Q132

The average starting salary of students who graduated from colleges of Business in 2009 was $48,400. A sample of 100 graduates of 2010 showed an average starting salary of $50,000. Assume the standard deviation of the population is known to be $8,000. We want to determine whether or not there has been a significant increase in the starting salaries.
a. State the null and alternative hypotheses to be tested.
b. Compute the test statistic.
c. The null hypothesis is to be tested at 95% confidence. Determine the critical value for this test.
d. What do you conclude?
e. Compute the p-value.

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Q133 Q133 Q133

The average price of homes sold in the U.S. in the past year was $220,000. A random sample of 81 homes sold this year showed an average price of $210,000. It is known that the standard deviation of the population is $36,000. At 95% confidence test to determine if there has been a significant decrease in the average price homes.
a. State the null and alternative hypotheses to be tested.
b. Compute the test statistic.
c. Determine the critical value for this test.
d. What do you conclude?
e. Compute the p-value.

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