500 câu trắc nghiệm Kinh tế lượng – 7C

Formulate the indicated conclusion in nontechnical terms. Be sure to address the orginal claim

7) The owner of a football team claims that the average attendance at games is over 532, and he is therefore justified in moving the team to a city with a larger stadium. 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 mean attandance is greater than 532.
○ There is sufficent evidence to support the claim that the mean attandance is greater than 532.
○ There is not sufficent evidence to support the claim that the mean attandance is less than 532.
○ There is sufficent evidence to support the claim that the mean attandance is less than 532.

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

8) The manufacturer of a refrigerator system for beer kegs procedures refrigerators that are supposed to maintain a true mean temperature, \(\mu \), of 46oF, ideal for a certain type of German pilsner. The owner of the brewery does not agree with the refrigerator manufacturer, and claims he can prove that the true mean temperature is incorrect.
○ The error of failing to reject the hypothesis that the mean temperature equals 46oF when it is really different from 46oF
○ The error of rejecting the hypothesis that the mean temperature equals 46oF when it is really different from 46oF
● The error of rejecting the hypothesis that the mean temperature equals 46oF when it is really equal from 46oF

Solve the problem

9) In a hypothesis test, which of the following will cause a decrease in \(\beta \), the probability of making a type II error?
A: Increasing \(\alpha \) while keeping the sample size n, fixed
B: Increasing the sample size n, while keeping \(\alpha \) fixed
C: Decreasing \(\alpha \) while keeping the sample size n, fixed
D: Decreasing the sample size n, while keeping \(\alpha \) fixed

● A and B
○ A and D
○ C and D
○ B and C

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.

10) According to a recent poll 53% of Americans would vote for the incumbent president. If a random sample of 100 people results in 45% who would vote for the incumbent, test the claim that the actual percentage is 53%. Use a 0.10 significane level.

H0: p = 0.53; H1: p \( \ne \) 0.53; Test statistics: z = -1.60; p-value = 0.1096
Critical value: z = ±1.645. Fail to reject H0. There is not sufficent sample evidence to warrant rejection of the claim that the actual percentage is 53%.

The sample data support the researcher’s claim that the proportion for the fathers in Littleon is higher than 34%.

11) In a sample of 163 children selected randomly from one town, it is found that 37 of them suffer asthma. At the level 0.05 significane level, test the claim that the population of all children in the town who suffer from asthma is 11%.

H0: p = 0.11; H1: p \( \ne \) 0.11; Test statistics: z = 4.77; p-value = 0.0002
Critical value: z = ±1.96. Reject H0. There is sufficent evidence to warrant rejection of the claim that the proportion of all children in the town who suffer from ashima is 11%.

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 manufacturer claims that fewer than 6% of its fax machine are defective. In a random sample of 97 such fax machines, 5% are defective. Find the p-value for a test of the manufacturer’s claim
○ 0.1763
○ 0.3264
○ 0.1591
● 0.3049

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) A random sample of 100 pumpkins is obatained and the mean circumference is found to be 40.5 cm. Assuming that the population standard deviation is known to be 1.6 cm. Use a 0.05 significane level to test the claim that the mean circumference of all pumpkins is equal to 39.9 cm.

H0: \(\mu \) = 39.9; H1: \(\mu \) \( \ne \) 39.9. Test statistics, z = 3.75, p-value = 0.0002. Because p-value of 0.0002 is less than significane level of \(\alpha \) = 0.05, we fail to reject the null hypothesis. There is sufficent evidence to warrant rejection of the claim that the mean of all pumpkins equals 39.9 cm.