Question 1

The average manufacturing work week in metropolitan Chattanooga was 40.2 hours last year. It is believed that the recession has led to a reduction in the average work week. To test the validity of this belief, the hypotheses are A) H₀: μ < 40.2 H_a: μ ≥ 40.2. B) H₀: μ ≥ 40.2 H_a: μ < 40.2. C) H₀: μ > 40.2 H_a: μ ≤ 40.2. D) H₀: μ = 40.2 H_a: μ ≠ 40.2.

Accepted Answer

The null hypothesis (HS) should always contain an equal sign. Hence, options A, C, and D can be ruled out.
The belief is that the average work week has reduced. Hence, the alternative hypothesis (Ha) should have a less than sign (<). Thus, option B is the correct choice.

Question 2

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 A) H₀: p > .75 H_a: p .75. B) H₀: p < .75 H_a: p .75. C) H₀: p .75 H_a: p < .75. D) H₀: p .75 H_a: p > .75.

Accepted Answer

The answer of In the past, 75% of the tourists...

Question 3

Read the z statistic from the normal distribution table and choose the correct answer. For a one-tailed test (lower tail) using α = .005, z =
A) -2.575.
B) -1.645.
C) 2.575.
D) 1.645.

Accepted Answer

For a one-tailed test with α = .005 and a lower tail, we need to find the z value that corresponds to the area of .005 in the tail of the standard normal distribution. Looking at the z-table, we can see that the closest value to .005 is .0049, which corresponds to a z-score of -2.575. Therefore, the correct choice is A.

Question 4

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 A) H₀: μ < 40,000 H_a: μ 40,000. B) H₀: μ 40,000 H_a: μ > 40,000. C) H₀: μ > 40,000 H_a: μ 40,000. D) H₀: μ 40,000 H_a: μ < 40,000.

Accepted Answer

The null hypothesis (H0) is that the average life expectancy of the tires is still 40,000 miles or less. The alternative hypothesis (Ha) is that the average life expectancy has increased, indicating a one-tailed test. The correct set of hypotheses is H₀: μ 11eb12c9_c698_2c2e_b394_d942ae189153_TB6985_11 40,000 H_a: μ > 40,000.

Question 5

Read the z statistic from the normal distribution table and choose the correct answer. For a one-tailed test (upper tail) at α = .0630, z =
A) -1.53.
B) 0.335.
C) -0.335.
D) 1.53.

Accepted Answer

To find the z statistic for an upper-tailed test, we need to look for the closest probability to α in the body of the normal distribution table. In this case, we need to look for the probability closest to 0.0630 in the upper tail of the table. The closest probability is 0.0628, which corresponds to a z score of 1.53. Therefore, the correct answer is D.

Question 6

Read the t statistic from the t distribution table and choose the correct answer. For a one-tailed test (upper tail), using a sample size of 14, and at the 5% level of significance, t =
A) 1.761.
B) -1.761.
C) -1.771.
D) 1.771.

Accepted Answer

For a one-tailed test at the 5% level of significance with a sample size of 14, the degrees of freedom (df) would be 13 (since df = sample size - 1). Looking up the t distribution table for df = 13 at the 5% level for a one-tailed test, the t value is 1.771.

Question 7

A two-tailed test is performed at the .05 level of significance. The p-value is determined to be .01. The null hypothesis
A) must be rejected.
B) should not be rejected.
C) could be rejected, depending on the sample size.
D) has been designed incorrectly.

Accepted Answer

The p-value of .01 is less than the level of significance of .05, indicating that the results are statistically significant. Therefore, the null hypothesis must be rejected.

Question 8

In a one-tailed hypothesis test (lower tail), the test statistic is determined to be 2. The p-value for this test is
A) .9772.
B) .0228.
C) .0056.
D) .5228.

Accepted Answer

In a one-tailed (lower tail) hypothesis test, a test statistic of 2 typically corresponds to a high p-value because it indicates the observed result is far to the right of the mean in a standard normal distribution. The exact p-value depends on the distribution being used, but for a standard normal distribution, a test statistic of 2 would correspond to the area to the right of 2, which is approximately 0.9772, indicating that the result is not in the lower tail of the distribution.

Question 9

A juice drink filling machine, when in perfect adjustment, fills the bottles with 12 ounces of drink on an average. Any overfilling or underfilling 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 A) H₀: μ < 12 H_a: μ ≥ 12. B) H₀: μ 12 H_a: μ > 12. C) H₀: μ ≠ 12 H_a: μ = 12. D) H₀: μ = 12 H_a: μ ≠ 12.

Accepted Answer

The answer of A juice drink filling machine, when in...

Question 10

A machine is designed to fill toothpaste tubes, on an average, with 5.8 ounces of toothpaste. The manufacturer does not want any underfilling or overfilling. The correct hypotheses to be tested are A) H₀: μ ≠ 5.8 H_a: μ = 5.8. B) H₀: μ = 5.8 H_a: μ ≠ 5.8. C) H₀: μ > 5.8 H_a: μ ≤ 5.8. D) H₀: μ ≥ 5.8 H_a: μ < 5.8.

Accepted Answer

The correct hypotheses to be tested are usually stated as:
Null hypothesis (H0): The mean amount of toothpaste filled in the tubes is equal to 5.8 ounces.
Alternative hypothesis (Ha): The mean amount of toothpaste filled in the tubes is not equal to 5.8 ounces.
Therefore, choice B is the best option as it correctly states the null and alternative hypotheses for the test.

Question 11

Read the t statistic from the t distribution table and choose the correct answer. For a one-tailed test (upper tail) with a sample size of 16 and at the .10 level, t =
A) 1.341.
B) -1.341.
C) -1.753.
D) 1.753.

Accepted Answer

For a one-tailed test at the .10 level with a sample size of 16, the degrees of freedom (df) would be 15 (since df = sample size - 1). Looking up the t distribution table for df = 15 at the .10 level for a one-tailed test, the t value is 1.341.

Question 12

The average monthly rent for one-bedroom apartments in Chattanooga has been $800. Because of the downturn in the real estate market, it is believed that there has been a decrease in the average rental. The correct hypotheses to be tested are A) H₀: μ ≥ 800 H_a: μ < 800. B) H₀: μ = 800 H_a: μ ≠ 800. C) H₀: μ > 800 H_a: μ ≤ 800. D) H₀: μ < 800 H_a: μ ≥ 800.

Accepted Answer

The null hypothesis (H0) should state that there is no change or the situation is as it was, which in this case is μ ≥ 800, indicating the average rent has not decreased. The alternative hypothesis (Ha) should reflect the belief or what is being tested for, which is μ < 800, indicating a decrease in average rent.

Question 13

Read the t statistic from the t distribution table and choose the correct answer. For a one-tailed test (lower tail), using a sample size of 14, and at the 5% level of significance, t =
A) 1.771.
B) 1.761.
C) -1.771.
D) -1.762.

Accepted Answer

The critical t-value for a one-tailed test with 13 degrees of freedom at the 5% level of significance (lower tail) is -1.771. The closest value in the table is -1.76, but because we are looking for a lower tail, we need to use the more negative value of -1.771. Therefore, the correct choice is C.

Question 14

For a one-tailed hypothesis test (upper tail), the p-value is computed to be .034. If the test is being conducted at the 1% level of significance, the null hypothesis
A) could be rejected or not rejected depending on the sample size.
B) could be rejected or not rejected depending on the sample mean.
C) is not rejected.
D) is rejected.

Accepted Answer

The p-value of .034 is greater than the 1% level of significance (0.01), meaning there is not enough evidence to reject the null hypothesis at this level of significance.

Question 15

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 hourly wage of computer programmers. To test whether or not there has been an increase, the correct hypotheses to be tested are A) H₀: μ < 21.80 H_a: μ ≥ 21.80. B) H₀: μ = 21.80 H_a: μ ≠ 21.80. C) H₀: μ > 21.80 H_a: μ ≤ 21.80. D) H₀: μ ≤ 21.80 H_a: μ > 21.80.

Accepted Answer

The null hypothesis (H0) should reflect no change or the status quo, which in this case is the average hourly wage being $21.80 or less, and the alternative hypothesis (Ha) should reflect the claim to be tested, which is an increase in the average hourly wage, hence μ > 21.80.

Question 16

Read the z statistic from the normal distribution table and choose the correct answer. For a two-tailed test using α = .0150, z =
A) 1.96.
B) 2.17.
C) -2.17.
D) -125.

Accepted Answer

For a two-tailed test with α = .0150, we must look for the area of .0075 in each tail. From the normal distribution table, the closest value for this area is 2.17. However, since it is a two-tailed test, we also need to consider the negative side of the distribution, which gives us a z value of -2.17 (since the table is symmetric). Thus, the z statistic for a two-tailed test using α = .0150 is either 2.17 or -2.17, depending on the direction of the test.

Question 17

The academic planner of a university thinks that at least 35% of the entire student body attends summer school. The correct set of hypotheses to test his belief is A) H₀: p < .35 H_a: p .35. B) H₀: p .35 H_a: p > .35. C) H₀: p .35 H_a: p < .35. D) H₀: p > .35 H_a: p .35.

Accepted Answer

The null hypothesis (H0) should be the belief that the planner wants to test, which is that at least 35% of the entire student body attends summer school. Therefore, the correct set of hypotheses should be:
H0: p >= .35
Ha: p < .35
Choice C has the correct format for the hypotheses with a null hypothesis greater than or equal to 0.35 and an alternative hypothesis less than 0.35. The other choices have either incorrect symbols or incorrect inequality directions for the null or alternative hypotheses.

Question 18

A student believes that the average grade on the final examination in statistics is at least 85. She plans on taking a sample to test her belief. The correct set of hypotheses is A) H₀: μ < 85 H_a: μ 85. B) H₀: μ 85 H_a: μ > 85. C) H₀: μ 85 H_a: μ < 85. D) H₀: μ > 85 H_a: μ 85.

Accepted Answer

The answer of A student believes that the average grade...

Question 19

Read the t statistic from the t distribution table and circle the correct answer. For a one-tailed test (lower tail) with 22 degrees of freedom at α = .05, the value of t =
A) 1.717.
B) 1.721.
C) -1.717.
D) -1.721.

Accepted Answer

To find the critical value for a one-tailed test with a lower tail, look for the closest value to .05 in the alpha column of the t distribution table. For 22 degrees of freedom, the closest value is .025. The corresponding t value in the table for .025 at 22 degrees of freedom is -1.717. Therefore, the answer is C.

Question 20

In a two-tailed hypothesis test, the test statistic is determined to be z = 2.5. The p-value for this test is
A) .9876.
B) .4938.
C) .0062.
D) .0124.

Accepted Answer

The answer of In a two-tailed hypothesis test, the test...

Quiz 9: Hypothesis Tests

The average manufacturing work week in metropolitan Chattanooga was 40.2 hours last year. It is believed that the recession has led to a reduction in the average work week. To test the validity of this belief, the hypotheses are

Read the z statistic from the normal distribution table and choose the correct answer. For a one-tailed test (lower tail) using α = .005, z =

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

Read the z statistic from the normal distribution table and choose the correct answer. For a one-tailed test (upper tail) at α = .0630, z =

Read the t statistic from the t distribution table and choose the correct answer. For a one-tailed test (upper tail) , using a sample size of 14, and at the 5% level of significance, t =

A two-tailed test is performed at the .05 level of significance. The p-value is determined to be .01. The null hypothesis

In a one-tailed hypothesis test (lower tail) , the test statistic is determined to be 2. The p-value for this test is

A juice drink filling machine, when in perfect adjustment, fills the bottles with 12 ounces of drink on an average. Any overfilling or underfilling 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

A machine is designed to fill toothpaste tubes, on an average, with 5.8 ounces of toothpaste. The manufacturer does not want any underfilling or overfilling. The correct hypotheses to be tested are

Read the t statistic from the t distribution table and choose the correct answer. For a one-tailed test (upper tail) with a sample size of 16 and at the .10 level, t =

The average monthly rent for one-bedroom apartments in Chattanooga has been $800. Because of the downturn in the real estate market, it is believed that there has been a decrease in the average rental. The correct hypotheses to be tested are

Read the t statistic from the t distribution table and choose the correct answer. For a one-tailed test (lower tail) , using a sample size of 14, and at the 5% level of significance, t =

For a one-tailed hypothesis test (upper tail) , the p-value is computed to be .034. If the test is being conducted at the 1% level of significance, the null hypothesis

Read the z statistic from the normal distribution table and choose the correct answer. For a two-tailed test using α = .0150, z =

The academic planner of a university thinks that at least 35% of the entire student body attends summer school. The correct set of hypotheses to test his belief is

A student believes that the average grade on the final examination in statistics is at least 85. She plans on taking a sample to test her belief. The correct set of hypotheses is

Read the t statistic from the t distribution table and circle the correct answer. For a one-tailed test (lower tail) with 22 degrees of freedom at α = .05, the value of t =

In a two-tailed hypothesis test, the test statistic is determined to be z = 2.5. The p-value for this test is