Kinh tế lượngTrắc nghiệm

500 câu trắc nghiệm Kinh tế lượng – 7B

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Determine whether the hypothesis test involves a sampling distribution of means that is a normal distribution, Student t distribution, or neither.

14) Claim \(\mu \) = 111. Sample data: n = 10, \({\bar x}\) = 101, s = 15.3. The sample data appear to come from a normally distribution with unknown \(\mu \) and \(\sigma \).
○ Normal
● Student t
○ Neither

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Assume that a simple random sample has been selected from a normally distributed population. Find the test statistics, p-value, critical value(s), and state the final conclusion.

15) Test the claim that the mean age of the prison population in one city is less than 26 years. Sample data are summarized as n = 25, \({\bar x}\) = 24.4 years, and s = 9.2 years. Use a significane level of \(\alpha \) = 0.05

\(\alpha \) = 0.05, Test statistics, t = -0.870, p-value = 0.1966. Critical value, t = -1.711. Because the test statistics is greater than alpha level, we fail to reject the null hypothesis. There is not sufficent sample evidence to support the claim that the mean age is less than 26 years.

Test the given claim using the traditional method of hypothesis testing. Assume that the sample has been randomly selected from a population with a normal distribution.

16) A test of sobriety involves measuring the subject’s motor skills. Twenty randomly selected sober subjects take the test and procedure a mean score of 41.0 with a standard deviation of 3.7. At the 0.01 level of significane, test the claim that the true mean score for all sober subjects is equal to 35.0

Test statistics, t = 7.252, Critical value, t = ±2.861. Reject the null hypothesis. There is sufficent evidence to warrant rejection of the claim that \(\mu \) = 35.0

17) A public bus company offical claims that the mean waiting time for bus number 14 during peak hours is less than 10 minutes. A college student took bus number 14 during peak hours on 18 different occasions. Her mean waiting time was 7.4 minutes with a standard deviation of 1.7 minutes. At the 0.01 level of significane level, test the claim that mean is less than 10 minutes.

Test statistics, t = -6.489, Critical value, t = -2.567. Reject H0: \(\mu \) = 10 minutes. The sample data support the claim that the mean waiting times is less than 10 minutes.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Find the critical value or values of \({\chi ^2}\) based on the given information.

18) H1: \(\sigma \) < 0.629, n = 19, \(\alpha \) = 0.025
● 8.231
○ 7.015
○ 31.526
○ 8.907

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Use the traditional method to test the given hypothesis. Assume that the population is normally distributed and that the sample has been randomly selected.

19) When 12 bolts are tested for hardness, their indexes have a standard deviation of 41.7. Test the claim that the standard deviation of the hardness indexes for all such bolts is greater than 30.0. Use a 0.025 level of significane.

Test statistics: \(\chi _{n – 1}^2 = \frac{{(n – 1){s^2}}}{{{\sigma ^2}}}\) = 21.253; Critical value: \({\chi ^2}\) = 21.920. Fail to reject H0. There is not sufficent sample evidence to support the claim that the standard deviation of all such bolts is greater than 30.0

20) A machine dispenses a liquid drug into bottles in such a way that standard deviation of the contents is 81 mililiters. A new machine is tested on a sample of 24 containers and the standard deviation for this sample group found to be 26 mililiters. At the level 0.05 of significane, test the claim that the amounts dispensed by the new machine have a smaller standard deviation.

Test statistics: \(\chi _{n – 1}^2 = \frac{{(n – 1){s^2}}}{{{\sigma ^2}}}\) = 2.370; Critical value: \({\chi ^2}\) = 13.091. Reject H0. The sample data support the claim that the new machine procedures a lower standard deviation.

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