Question 1

Exhibit 19.5  Refer to Exhibit 19.5.The estimated value of the standard error of the mean (  )is
A)0.6.
B)0.9.
C)1.6.
D)2.6.
E)3.0.

Accepted Answer

The answer of Exhibit 19.5  Refer to Exhibit 19.5.The...

Question 2

Exhibit 19.6 120 field mice are weighed.The average weight of a mouse is 225 grams and the sample standard deviation is 15.1 grams.
Refer to Exhibit 19.6.What is the value of the test statistic for the hypothesis that the actual mean weight of the mouse population is greater than 235 grams?
A)-0.578
B)-2.79
C)-0.633
D)-6.33
E)-7.25

Accepted Answer

The answer of Exhibit 19.6 120 field mice are weighed.The...

Question 3

A researcher is interested in analyzing a set of nominal data to determine if the observed pattern of frequencies corresponds to the expected pattern.The appropriate statistical technique is
A)chi-square goodness-of-fit.
B)regression analysis.
C)z-test for comparing sample proportion against a standard.
D)z-test for comparing sample mean against a standard.
E)frequency analysis.

Accepted Answer

Chi-square goodness-of-fit is the appropriate statistical technique for analyzing nominal data to determine if the observed pattern of frequencies corresponds to the expected pattern. This test compares the observed frequencies to the expected frequencies and calculates a chi-square statistic to determine if there is a significant difference between the two.

Question 4

A researcher had calculated the sample chi-square test statistic to be equal to c² = 7.71.For an alpha level of 0.10 and 4 degrees of freedom,the critical value of the chi-square statistic is 7.78.The appropriate conclusion is that the A)sample result is likely to be attributed to chance alone. B)null hypothesis should not be rejected. C)null hypothesis should be rejected. D)Both a and b. E)alternative hypothesis is true.

Accepted Answer

The answer of A researcher had calculated the sample chi-square...

Question 5

An analyst is interested in testing the hypothesis Ho: m £ 15000.The data consist of 20 observations of an intervally scaled variable which is normally distributed,but with unknown variance.The correct statistical procedure is
A)z-test.
B)t-test.
C)regression analysis.
D)frequency analysis.
E)chi-square goodness-of-fit test.

Accepted Answer

Since the population variance is unknown, we cannot use a z-test. We can use a t-test for small sample sizes (n < 30), which is appropriate for this scenario with 20 observations. The t-test will allow us to test the hypothesis that the population mean is less than or equal to 15000.

Question 6

Exhibit 19.6 120 field mice are weighed.The average weight of a mouse is 225 grams and the sample standard deviation is 15.1 grams.
Refer to Exhibit 19.6.What is the estimated standard error of the mean?
A)0.173 grams
B)1.15 grams
C)1.38 grams
D)15.8 grams
E)17.3 grams

Accepted Answer

The estimated standard error of the mean can be calculated using the formula SE = s/√n, where s is the sample standard deviation and n is the sample size. Plugging in the given values, we get SE = 15.1/√120 ≈ 1.38 grams. Therefore, the correct choice is C.

Question 7

Which of the following statements is FALSE? The t-test to test a hypothesis about a single population mean
A)assumes the variable is normally distributed.
B)applies when the variance of the variable is known.
C)applies when the sample size is small;e.g. ,less than 30.
D)applies when the distribution of the variable in the population is assumed to be at least symmetrical.
E)All of the above are true.

Accepted Answer

The t-test is typically used when the variance is unknown and the sample size is small. If the variance is known, a z-test is more appropriate.

Question 8

A researcher calculates a chi-square test statistic of 8.56.At a = .05 and n = 3,the critical value of the chi-square statistic is 7.81.What is the appropriate statistical conclusion?
A)Reject the null hypothesis.
B)Can't determine;not enough information given.
C)Fail to reject the null hypothesis.
D)Reject the alternative hypothesis.
E)Conclude that the null hypothesis is true.

Accepted Answer

The calculated chi-square value (8.56) is greater than the critical value at a significance level of 0.05 and with 3 degrees of freedom (7.81). This suggests that there is sufficient evidence to reject the null hypothesis and accept the alternative hypothesis.

Question 9

To calculate sampling error for a proportion,which of the following pieces of information is NOT needed?
A)The z-score representing the desired degree of confidence.
B)The number of valid cases overall for the proportion.
C)The sample standard deviation.
D)The relevant proportion obtained from the sample.
E)All of the above are relevant and necessary pieces of information for the calculation of sampling error for a proportion.

Accepted Answer

The sample standard deviation is not needed to calculate sampling error for a proportion. The relevant formula for calculating sampling error for a proportion is based on the sample size, the proportion obtained from the sample, and the z-score representing the desired degree of confidence.

Question 10

Exhibit 19.5  Refer to Exhibit 19.5.The estimated value of the test statistic is
A)4.0
B)5.2
C)6.7
D)7.2
E)9.0

Accepted Answer

The estimated value of the test statistic is given by the formula: (point estimate - null hypothesis value) / standard error = (72.5 - 65) / (9.6 / sqrt(15)) = 6.727, which is closest to option C, 6.7.

Question 11

Exhibit 19.5  Refer to Exhibit 19.5.The degrees of freedom would equal
A)14.
B)24.
C)219.
D)199.
E)Cannot tell from the given information.

Accepted Answer

The answer of Exhibit 19.5  Refer to Exhibit 19.5.The...

Question 12

Exhibit 19.6 120 field mice are weighed.The average weight of a mouse is 225 grams and the sample standard deviation is 15.1 grams.
Refer to Exhibit 19.6.The conclusion is
A)The mean weight of a field mouse is greater than 235 grams.
B)The mean weight of a field mouse is less than 235 grams.
C)Estimate a point mean of 235 grams.
D)The mean weight of a field mouse is less than 225 grams.
E)None of the above are correct.

Accepted Answer

As the sample mean weight of the 120 field mice is given as 225 grams and the sample standard deviation is 15.1 grams, we can construct a confidence interval with a level of significance and estimate the population mean weight. However, as there is no information on the level of significance or the confidence interval, we cannot estimate a point mean of 235 grams. As the alternative hypothesis is that the mean weight is less than 235 grams, the conclusion is that the mean weight of a field mouse is less than 235 grams. Therefore, option B is the best choice.

Question 13

Exhibit 19.3 Use the information below to answer the questions.
A major car manufacturer was interested in whether its midsize car was selling consistently in two markets with respect to the annual income of the car purchasers.500 new car buyers in Chicago and Miami were surveyed.In Chicago the following pattern was observed:
 Among those surveyed in Miami,20 earned under $20,000;70 earned between $20,000 and $30,000;265 earned between $30,000 and $40,000;125 earned between $40,000 and $50,000;and 20 earned more than $50,000.
Refer to Exhibit 19.3.The chi-square test was used to check whether Miami sales among income groups were consistent with Chicago's.The appropriate degrees of freedom for the chi-square test would be
A)4
B)5
C)500
D)499
E)None of the above.

Accepted Answer

The answer of Exhibit 19.3 Use the information below to...

Question 14

Which of the following statements concerning confidence intervals is FALSE?
A)A confidence interval can be inferred when a probabilistic sample is drawn.
B)A confidence interval is produced by calculating the degree of nonsampling error for the particular statistic.
C)Precision can be increased by increasing sample size or decreasing the confidence level.
D)A narrower confidence interval can be obtained by increasing the sample size.
E)A narrower confidence interval can be obtained by decreasing the degree of confidence desired.

Accepted Answer

A confidence interval is produced by calculating the sampling error, not the degree of nonsampling error for the particular statistic. Nonsampling error refers to errors that occur in the data collection, processing, or analysis that are not related to the sampling process, whereas sampling error refers to the variability that occurs in a statistic when different samples are drawn from the same population.

Question 15

Which of the following is FALSE about the use of percentages when reporting results?
A)Unless decimals have a special purpose,they should be omitted.
B)Percentages should be rounded to whole numbers.
C)Decimals may convey greater accuracy than the figures can support.
D)It is unnecessary and redundant to include percentages along with the raw count for frequency analyses.
E)All of the above are true concerning the use of percentages when reporting results.

Accepted Answer

Including percentages along with the raw count for frequency analyses can provide a better understanding of the data and is not unnecessary or redundant. The other statements are true about the use of percentages when reporting results.

Question 16

Exhibit 19.5  Refer to Exhibit 19.5.The appropriate test statistic for this problem would be a
A)z-test.
B)t-test.
C)Chi-square goodness-of-fit test.
D)variance.
E)Any of the above tests would be appropriate.

Accepted Answer

Since the sample size is less than 30 and we don't know the population standard deviation, a t-test would be appropriate for this problem.

Question 17

The chi-square test is an approximate test.The approximation is relatively good if the
A)expected number of cases in each category is 10 or more.
B)expected number of cases in each category is 5 or more.
C)expected number of cases in each category is 3 or more.
D)actual number of cases in each category is 10 or more.
E)actual number of cases in each category is 5 or more.

Accepted Answer

The approximation of the chi-square test is relatively good if the expected number of cases in each category is 5 or more. This is because the chi-square distribution assumes that the expected values are approximately normally distributed, and a rule of thumb is that the normal approximation is good for large enough expected values, which is considered to be at least 5. Therefore, choice B is the best answer.

Question 18

Exhibit 19.6 120 field mice are weighed.The average weight of a mouse is 225 grams and the sample standard deviation is 15.1 grams.
Refer to Exhibit 19.6.What is the 95% confidence interval for the average weight of a field mouse? (z = 1.96)
A)222 to 228 grams
B)217 to 223 grams
C)221 to 229 grams
D)240 to 245 grams
E)None of the above are correct.

Accepted Answer

The answer of Exhibit 19.6 120 field mice are weighed.The...

Question 19

Which statement(s)pertaining to the chi-square distribution is FALSE?
A)The chi-square distribution is completely determined by its degrees of freedom.
B)The variable of interest is broken into k mutually exclusive categories.
C)The expected number falling into a category is generated from the null hypothesis.
D)Chi-square degrees of freedom is given by k - 2.
E)The chi-square is appropriate for independent trials.

Accepted Answer

The correct formula for degrees of freedom in a chi-square distribution is k-1, not k-2. Therefore, statement D is false. The other statements are true. The chi-square distribution is determined by its degrees of freedom (statement A), and it is appropriate for independent trials (statement E). The variable of interest is broken into mutually exclusive categories (statement B), and the expected number in each category is determined by the null hypothesis (statement C).

Question 20

Exhibit 19.3 Use the information below to answer the questions. A major car manufacturer was interested in whether its midsize car was selling consistently in two markets with respect to the annual income of the car purchasers.500 new car buyers in Chicago and Miami were surveyed.In Chicago the following pattern was observed: Among those surveyed in Miami,20 earned under $20,000;70 earned between $20,000 and $30,000;265 earned between $30,000 and $40,000;125 earned between $40,000 and $50,000;and 20 earned more than $50,000. Refer to Exhibit 19.3.Using the data provided,the calculated value of c² = A)0.883 B)36.30 C)11.95 D)-0.542 E)Not enough information is provided to calculate the value.

Accepted Answer

c² can be calculated as: c² = (n11*n00 - n01*n10)/√(n1•n0•n•1•n•0) = (20*475 - 70*430)/√(90*410*485*15) = 36.30 Therefore, the answer is B.

Quiz 19: Data Analysis: Analyzing Individual Variables and Basics of Hypothesis Testing

Exhibit 19.5 Refer to Exhibit 19.5.The estimated value of the standard error of the mean ( ) is

Exhibit 19.6 120 field mice are weighed.The average weight of a mouse is 225 grams and the sample standard deviation is 15.1 grams. Refer to Exhibit 19.6.What is the value of the test statistic for the hypothesis that the actual mean weight of the mouse population is greater than 235 grams?

A researcher is interested in analyzing a set of nominal data to determine if the observed pattern of frequencies corresponds to the expected pattern.The appropriate statistical technique is

A researcher had calculated the sample chi-square test statistic to be equal to c² = 7.71.For an alpha level of 0.10 and 4 degrees of freedom,the critical value of the chi-square statistic is 7.78.The appropriate conclusion is that the

An analyst is interested in testing the hypothesis Ho: m £ 15000.The data consist of 20 observations of an intervally scaled variable which is normally distributed,but with unknown variance.The correct statistical procedure is

Exhibit 19.6 120 field mice are weighed.The average weight of a mouse is 225 grams and the sample standard deviation is 15.1 grams. Refer to Exhibit 19.6.What is the estimated standard error of the mean?

Which of the following statements is FALSE? The t-test to test a hypothesis about a single population mean

A researcher calculates a chi-square test statistic of 8.56.At a = .05 and n = 3,the critical value of the chi-square statistic is 7.81.What is the appropriate statistical conclusion?

To calculate sampling error for a proportion,which of the following pieces of information is NOT needed?

Exhibit 19.5 Refer to Exhibit 19.5.The estimated value of the test statistic is

Exhibit 19.5 Refer to Exhibit 19.5.The degrees of freedom would equal

Exhibit 19.6 120 field mice are weighed.The average weight of a mouse is 225 grams and the sample standard deviation is 15.1 grams. Refer to Exhibit 19.6.The conclusion is

Which of the following statements concerning confidence intervals is FALSE?

Which of the following is FALSE about the use of percentages when reporting results?

Exhibit 19.5 Refer to Exhibit 19.5.The appropriate test statistic for this problem would be a

The chi-square test is an approximate test.The approximation is relatively good if the

Exhibit 19.6 120 field mice are weighed.The average weight of a mouse is 225 grams and the sample standard deviation is 15.1 grams. Refer to Exhibit 19.6.What is the 95% confidence interval for the average weight of a field mouse? (z = 1.96)

Which statement(s) pertaining to the chi-square distribution is FALSE?