Ch11 - ch 11 prep questions PDF

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ch11 Student:

1. Statistical inferences regarding σ2 are based on the F distribution. True False 2. The population variance is one of the most widely used quantitative measures of risk in investments. True False 3. The skewness of the Chi-square probability distribution depends on the degrees of freedom. True False 4. The values of the True False

distribution range from negative infinity to infinity.

5. The formula for the confidence interval of the population variance σ2 is valid for the random samples drawn from any population. True False 6. The value of the test statistic for the hypothesis test of the population variance, σ2 is computed as True False

.

7. The null hypothesis True False

is rejected if the value of the test statistic exceeds

.

8. The parameter of interest for inferences regarding the ratio of two population variances is their sum . True False 9. The estimator of . True False

used in the inference regarding the ratio of two population variances is

10. The sampling distribution of True False

is the χ2 distribution.

11. The distribution is positively skewed. True False 12. The formula for constructing the confidence interval for the ratio of two population variances is based on the assumption that the sample variances are computed from independently drawn samples from two nonnormal populations. True False 13. A right-tailed test for the ratio of two population variances than . True False

examines whether

is greater

14.

15.

16.

17.

It is preferable to place the smaller sample variance in the numerator of the True False The value of the test statistic to test the ratio of two population variances is True False A distribution tends to the A. F distribution B. Uniform distribution C. Student's t distribution D. Normal distribution

.

, as the degrees of freedom increase.

If a sample of size n is taken from a normal population with a finite variance, then the statistic A. (n + 1) (n - 1) B. n + 1 C. n 1 D. n

18.

statistic.

follows the

distribution with degrees of freedom

.

If s2 is computed from a random sample of n observations drawn from an underlying normal population with a finite variance, then the A.

variable is defined as

.

B. C. D. 19.

20.

The is the probability distribution of the sum of several independent squared standard normal random variables. A. F distribution B. distribution C. Student's t distribution D. Uniform distribution Which of the following is the formula for the sample variance s2 when used as an estimate of σ2 for a random sample of n observations from a population? A. B. C. D.

21.

Statistical inferences pertaining to σ2 are based on which of the following distributions? A. The F distribution B. The Student's t distribution C. The Chi-Square distribution D. The normal distribution

22.

If P( ≥ x) = 0.05, then the value of x is A. 14.449 B. 10.645 C. 12.592 D. 1.6350

23.

.

Given below are the values taken from a normal population. A 95% confidence interval for the population variance is closest to: A. [2.03, 16.30] B. [10.12, 81.43] C. [9.00, 72.41] D. [11.39, 91.64]

24.

25.

26.

27.

28.

For a 99% confidence level find A. 16.812 B. 18.548 C. 0.872 D. 0.676

with 6 degrees of freedom.

Compute a 98% confidence interval for the population variance when the sample variance is 20 for a sample of 10 items from a normal population. A. 8.308 to 86.207 B. 7.476 to 77.512 C. 8.617 to 78.125 D. 7.755 to 70.313 Which of the following factors is used to conduct hypothesis tests regarding the population variance? A. Sample mean B. Population mean C. Sample proportion D. Sample variance Identify the hypothesis that depicts a right-tailed test for the population variance from the list of hypotheses given below. A. B. C. D. You want to test whether the population variance differs from 50. From a sample of 25 observations drawn from a normally distributed population, you calculate s2 = 80. When conducting this test at the 5% significance level, the value of test statistic, A. 5.625 B. 12.401 C. 14.400 D. 39.364

is:

29.

30.

31.

32.

For a sample of 10 observations drawn from a normally distributed population, we obtain the sample mean and the sample variance as 50 and 75, respectively. We want to determine whether the population variance is greater than 70. The critical value at a 5% significance level is: A. 1.645 B. 3.325 C. 9.642 D. 16.919 Which of the following is a feature of the F distribution? A. The F distribution depends on one degree of freedom. B. The F distribution is bell-shaped with values ranging from negative infinity to infinity. C. The F distribution becomes increasingly symmetric when the degrees of freedom increase. D. The F distribution is negatively skewed. We conduct the following hypothesis test: versus . For a random sample of 15 observations, the sample standard deviation is 12. Approximate the p-value used to conduct this test. A. p-value lies between 0.025 and 0.05 B. p-value lies between 0.01 and 0.025 C. p-value lies between 0.05 and 0.10 D. p-value is greater than 0.10 Students of two sections of a History course took a common final examination. The course instructor examines the variance in scores between the two sections. He selects random samples of n1 = 11 and n2 = 16 with sample variances of and , respectively. Assuming that the population distributions are normal, construct a 90% confidence interval for the ratio of the population variance. A. [0.90, 2.41] B. [0.50, 2.00] C. [0.25, 4.00] D. [0.79, 5.70]

33.

34.

Find the value of x for which A. 20.483 B. 18.307 C. 15.987 D. 4.1680

= 0.05.

Exhibit 11-1. Becky owns a diner and is concerned about sustaining the business. She wants to ascertain if the standard deviation of the profits for each week is greater than $250. The details of the profits for the week are listed below (in dollars.) Assume that profits are normally distributed. Refer to Exhibit 11-1. The appropriate null and alternate hypotheses are: A. B. C. D.

35.

Exhibit 11-1. Becky owns a diner and is concerned about sustaining the business. She wants to ascertain if the standard deviation of the profits for each week is greater than $250. The details of the profits for the week are listed below (in dollars.) Assume that profits are normally distributed. Refer to Exhibit 11-1. What is the value of the test statistic? A. 6.146 B. 8.604 C. 6.652 D. 7.375

36.

Exhibit 11-1. Becky owns a diner and is concerned about sustaining the business. She wants to ascertain if the standard deviation of the profits for each week is greater than $250. The details of the profits for the week are listed below (in dollars.) Assume that profits are normally distributed.

Refer to Exhibit 11-1. Test Becky's concern using the critical value approach at α = 0.05. What is the result? A. We reject H0 since the value of the test statistic is greater than

.

B. We do not reject H0 since the value of the test statistic is greater than C. We reject H0 since the value of the test statistic is less than

. .

D. We do not reject H0 since the value of the test statistic is less than 37.

38.

39.

.

A random sample of 18 observations is taken from a normal population. The sample mean and sample standard deviation are 76.4 and 4.2, respectively. What is an 80% interval estimate of the population variance? A. [12.107, 29.735] B. [10.870, 34.581] C. [12.819, 31.484] D. [14.636, 23.443] How does the width of the interval respond to the changes in the confidence interval? A. The width of the interval decreases with an increase in the confidence interval. B. The width of the interval increases with an increase in the confidence interval. C. The width of the interval is halved with the increase in the confidence interval. D. The width of the interval is doubled with the decrease in the confidence interval. Exhibit 11-2. The manager of a video library would like the variance of the waiting times of the customers not to exceed 2.30 minutes-squared. He would like to add an additional billing counter if the variance exceeds the cut-off. He checks the recent sample data. For a random sample of 24 customer waiting times, he arrives at a sample variance of 3.8 minutes-squared. The manager assumes the waiting times to be normally distributed. Refer to Exhibit 11-2. Which of the following would be null and the alternate hypothesis to test if the cutoff is surpassed? A. B. C. D.

40.

Exhibit 11-2. The manager of a video library would like the variance of the waiting times of the customers not to exceed 2.30 minutes-squared. He would like to add an additional billing counter if the variance exceeds the cut-off. He checks the recent sample data. For a random sample of 24 customer waiting times, he arrives at a sample variance of 3.8 minutes-squared. The manager assumes the waiting times to be normally distributed. Refer to Exhibit 11-2. Approximate the p-value. A. p-value lies between 0.005 and 0.010 B. p-value lies between 0.010 and 0.025 C. p-value lies between 0.050 and 0.10 D. p-value lies between 0.025 and 0.05

41.

Exhibit 11-2. The manager of a video library would like the variance of the waiting times of the customers not to exceed 2.30 minutes-squared. He would like to add an additional billing counter if the variance exceeds the cut-off. He checks the recent sample data. For a random sample of 24 customer waiting times, he arrives at a sample variance of 3.8 minutes-squared. The manager assumes the waiting times to be normally distributed. Refer to Exhibit 11-2. At α = 0.05 which of the following is the critical value, A. 13.091 B. 32.007 C. 35.172 D. 38.076

42.

43.

44.

45.

?

Which of the following Excel functions is used to calculate the exact probability for a left-tailed distribution? A. CHISQ.DIST (x, deg_ freedom,cumulative) B. CHISQ.DIST (x, n-2) C. CHISQ.DIST (x, n/2) D. CHISQ.DIST (x/2, deg_freedom, cumulative) Which of the following Excel functions is used to determine the left-tailed probability? A. CHISQ.INV (probability, n) B. CHISQ.INV (probability, n-2) C. CHISQ.INV (probability, deg_ freedom) D. CHISQ.INV (probability, n/2)

value given any

Which of the following characteristics is true with regard to the F distribution? A. The F(df1, df2) distribution is negatively skewed. B. The values of the F(df1, df2) distribution range from negative infinity to infinity. C. The F(df1, df2) distribution is the probability distribution of the ratio of two independent chi-square variables. D. The shape of the F(df1, df2) distribution is independent of the degrees of freedom. If independent samples of size n1 and n2 are drawn from normal populations with equal variances, then the value of the F(df1, df2) statistic is calculated as . A. B. C. D.

46.

47.

48.

The degrees of freedom df1 and df2 for an F(df1, df2) distribution is given by A. (n1 - 2); (n2 - 2) B. n2 (n1 - 2); n1(n2 - 2) C. (n1 - 1); (n2 - 1) D. n (n1 - 1); n (n2 1)

and

.

Find the value of x given the equation P(F(6, 10) ≥ x) = 0.025. A. 4.07 B. 5.46 C. 3.22 D. 5.39 Which of the following is the formula for a confidence interval for the ratio of the population variances A.

?

B.

C.

D.

49.

A professor analyzes the variance in scores between two sections that he teaches. The students of each section took the same test. The random samples drawn from the observations yield sample variances of = 203.15 and = 474.42 for samples of n1 = 13 and n2 = 16, respectively. Construct a 99% confidence interval for the ratio of the population variances. A. [0.1540, 2.7809] B. [0.1008, 2.0217] C. [0.1386, 3.0895] D. [0.0907, 1.8198]

50.

51.

A two-tailed test is used to determine if two population variances differ. The null hypothesis takes the form H0: A. B. C. D. The result of placing a larger sample variance in the numerator of the F(df1, df2) statistic allows us to A. focus only on the right tail of the distribution. B. arrive at a more accurate F(df1, df2) statistic value. C. focus only on the left tail of the distribution. D. determine if the distribution is symmetric.

52.

53.

54.

Which of the following Excel functions is used to calculate the right-tailed probability for a value x on the F(df1, df2) distribution? A. F.DIST.RT (x, deg_ freedom1, deg_ freedom2, cumulative) B. F.DIST.RT (x, n1, n2) C. F.DIST.RT (x, n1-2, n2-2) D. F.DIST.RT (x, deg_freedom1, deg_ freedom2) Which of the following Excel functions is used to obtain the right-tailed value for the F(df1, df2) statistic given any probability? A. F.INV.RT (probability, n1, n2) B. F.INV.RT (probability, deg_ freedom1, deg_ freedom2) C. F.INV.RT (probability, n1-2,n2-2) D. F.INV.RT (probability, deg_ freedom) Construct a 95% confidence interval for the ratios of two population variances. The random samples of n1 = 9 and n2 = 11 with sample variances of were drawn from a normal population. A. [0.50, 2.00] B. [0.52, 8.60] C. [0.25, 1.41] D. [0.44, 4.30]

55.

and

, respectively. Assume that the samples

Exhibit 11-3. The following are the competing hypotheses and the relevant summary statistics.

Sample 1:

n1 = 10

Sample 2:

n2 = 9

Refer to Exhibit 11-3. Which of the following statements is true with regard to the assumptions for conducting the hypothesis test? A. The samples are drawn from a nonnormal population. B. The samples are dependent and taken from a normal population. C. The difference of the sample variances is used to test the hypotheses. D. The samples are independent and taken from a normal population. 56.

Exhibit 11-3. The following are the competing hypotheses and the relevant summary statistics.

Sample 1:

n1 = 10

Sample 2:

n2 = 9

Refer to Exhibit 11-3. What is the critical value at the 5% significance level? A. 3.02 B. 3.14 C. 3.23 D. 3.39

57.

Exhibit 11-3. The following are the competing hypotheses and the relevant summary statistics.

Sample 1:

n1 = 10

Sample 2:

n2 = 9

Refer to Exhibit 11-3. The p-value associated with the value of the test statistic is 0.3692. At the 5% significance level, which of the following conclusions is correct? A. We reject the null hypothesis and conclude that the variances differ. B. We do not reject the null hypothesis and conclude that the variances differ. C. We reject the null hypothesis and cannot conclude that the variances differ. D. We do not reject the null hypothesis and cannot conclude that the variances differ. 58.

Consider the expected returns (in percent) from two investment options. Beth wants to determine if investment 1 has a lower variance. Use the following summary statistics to arrive at the results. Investment 1:

= 33.53; n1 = 8

Investment 2:

= 44.76; n2 = 8

Identify the relevant null and alternate hypotheses for this test. A. B. C. D. 59.

Exhibit 11-4. Consider the expected returns (in percent) from the two investment options. Beth claims that the variances of the returns for the two investments differ. Use the following data to arrive at the results.

Refer to Exhibit 11-4. Which of the following is the correct p-value? A. 0.2873 B. 0.7127 C. 0.3564 D. 0.6436 60.

Exhibit 11-4. Consider the expected returns (in percent) from the two investment options. Beth claims that the variances of the returns for the two investments differ. Use the following data to arrive at the results.

Refer to Exhibit 11-4. Test Beth's claim at the 5% significance level. What is the conclusion? A. p-value = 0.7127 > α = 0.05; Beth's claim is correct. B. p-value = 0.7127 > α = 0.05; Beth's claim is wrong. C. p-value = 0.7127 < α = 0.05; Beth's claim is wrong. D. p-value = 0.7127 < α = 0.05; Beth's claim is correct.

61. Exhibit 11-5. Amie Jackson, a manager at Sigma travel services, makes every effort to ensure that customers attempting to make online reservations do not have to wait too long to complete the reservation process. The travel website is open for reservations 24 hours a day, and Amie regularly checks the website for the waiting time to maintain consistency in service. She uses the following independently drawn samples of wait time during two peak hours, morning 8 am to 10 am and evening 7 pm to 9 pm, for the analysis. Assume that wait times are normally distributed.

Refer to Exhibit 11-5. Identify the 95% interval estimate for the ratio of the population variances. A. [1.02, 8.55] B. [1.00, 8.73] C. [0.99, 8.83] D. [1.19, 7.34] 62. Exhibit 11-5. Amie Jackson, a manager at Sigma travel services, makes every effort to ensure that customers attempting to make online reservations do not have to wait too long to complete the reservation process. The travel website is open for reservations 24 hours a day, and Amie regularly checks the website for the waiting time to maintain consistency in service. She uses the following independently drawn samples of wait time during two peak hours, morning 8 am to 10 am and evening 7 pm to 9 pm, for the analysis. Assume that wait times are normally distributed.

Refer to Exhibit 11-5. Construct a 90% confidence interval and test if the ratio of the population variances differs from one at the 10% significance level. Which of the following outcomes supports the test? A. [1.47, 5.99]. The ratio of the population variances differs from one at the 10% significance level. B. [1.19, 7.35]. The ratio of the population variances differs from one at the 10% significance level. C. [1.47, 5.99]. The ratio of the population variances does not differ from one at the 10% significance level. D. [1.19, 7.35]. The ratio of the population variances does not differ from one at the 10% significance level.

63. Exhibit 11-5. Amie Jackson, a manager at Sigma travel services, makes every effort to ensure that customers attempting to make online reservations do not have to wait too long to complete the reservation process. The travel website is open for reservations 24 hours a day, and Amie regularly checks the website for the waiting time to maintain consistency in service. She uses the following independently drawn samples of wait time during two peak hours, morning 8 am to 10 am and evening 7 pm to 9 pm, for the analysis. Assume that wait times are normally distributed.

Refer to Exhibit 11-5. State the null and the alternate hypotheses to determine if the variance of wait time during morning peak hours (population 1) differs from that during the evening peak hours (population 2). A. B. C. D. 64. Exhibit 11-5. Amie Jackson, a manager at Sigma travel services, makes every effort to ensure that customers attempting to make online reservations do not have to wait too long to complete the reservation process. The travel website is open for reservations 24 hours a day, and Amie regularly checks the website for the waiting time to maintain consistency in service. She uses the following independently drawn samples of wait time during two pea...