500 câu trắc nghiệm Kinh tế lượng – 7A

Formulate the indicated conclusion in nontechnical terms. Be sure to address the orginal claim
7) A researcher claims that the amounts of acetaminophen in a certain brand of cold tables have a standard deviation different from \(\sigma \) = 3.3 mg claimed by the manufacturer. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in nontechnical terms.
○ There is not sufficent evidence to support the claim that the standard deviation is equal to 3.3 mg
● There is not sufficent evidence to support the claim that the standard deviation is different from 3.3 mg
○ There is sufficent evidence to support the claim that the standard deviation is different from 3.3 mg
○ There is sufficent evidence to support the claim that the standard deviation is equal to 3.3 mg

Assume that a hypothesis test of the given claim will be conducted. Indentify the type I error of the test.

8) Carter Motor company claims that its new sedan, the Libra, will average better than 30 miles per gallon in the city. Indentify the type I error for the test.
○ The error of failing to reject the hypothesis that the mean is 30 miles per gallon when it is actually greater than 30 miles per gallon.
● The error of rejecting the hypothesis that the mean is 30 miles per gallon when it really is 30 miles per gallon.
○ The error of rejecting the hypothesis that the mean is more 30 miles per gallon when it really is more than 30 miles per gallon.

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

Solve the problem

9) Suppose that you perform a hypothesis test regarding a population mean, and that the evidence does not warrant rejection of null hypothesis. When formulating the conclusion to the test, why is the phrase “fail to reject the null hypothesis” more accurate than the phrase “accept the null hypothesis”?

In a hypothesis test, we do not prove the null hypothesis; we just determine whether we have sufficent evidence to reject the null hypothesis. If there is not sufficent evidence, this does not neccessarily imply that the null hypothesis is true but that we don’t have enough evidence to reject it.

Indentify the null hypothesis, alternative hypothesis, test statistics, p-value, conclusion about the null hypothesis, and final conclusion that address the orginal claim.

10) A supplier of 3.5″ disks claims that only 1% of the disks are defective. In a random sample of 600 disks, it is found that 3% are defective, but the supplier claims that is simple a sample fluctuation. At the 0.01 level of significane, test the supplier’s claim that 1% are defective.

H0: p = 0.01; H1: p \( \ne \) 0.01. Test statistics: z = 4.92, p-value = 0.0002. Critical value, z = ±2.575. Reject the null hypothesis. There is sufficent evidence to warrant rejection of the claim that 1% are defective.

11) A nationwide study of American homeowners revealed that 64% have one or more lawn mowers. A lawn equipment manufacturer, located in Omaha, claims the estimate is too low for households in Omaha. Can the value 0.64 be rejected if a survey of 496 homes in Omaha yields 335 with one or more lawn mowers? Use \(\alpha \) = 0.05.

H0: p = 0.64, H1: p > 0.64. Test statistics z = 1.643, p-value = 0.0505. Critical value z = 1.645. Fail to reject null hypothesis. There is not sufficent sample evidence to support the claim that the proportion with lawn mowers in Omaha is greater than 0.64.

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

Find p-value for the indicated hypothesis test

12) A medical school claims more than 28% of its students plan to go into general practice. It is found that among a random sample of 130 of the school’s student, 32% of them plan go into general practice. Find the p-value for a test of school’s claim.

● 0.1539
○ 0.1635
○ 0.3078
○ 0.3461

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

Indentify the null hypothesis, alternative hypothesis, test statistics, p-value, conclusion about the null hypothesis, and final conclusion that address the orginal claim.

13) Various temperature measurements are recorded at different times for a particular city. The mean of 25oC is obtained for 60 different days. Assuming that \(\sigma \) = 1.5oC, test the claim that the population mean is 22oC. Use 0.05 significane level.

H0: \(\mu \) = 22; H1: \(\mu \) \( \ne \) 22. Test statistics, z = 15.49, p-value = 0.0002. Because p-value of 0.0002 is less than significane level of \(\alpha \) = 0.05, we reject the null hypothesis. There is sufficent evidence to warrant rejection of the claim that the population mean is 22oC.