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500 câu trắc nghiệm Kinh tế lượng – 7B

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

7) A cereal company claims that the mean weight of the cereal in its packet is 14 oz. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms.
○ There is sufficent evidence to warrant rejection of the claim that the mean weight is less than 14 oz.
○ There is not sufficent evidence to warrant rejection of the claim that the mean weight is 14 oz.
● There is sufficent evidence to warrant rejection of the claim that the mean weight is 14 oz.
○ There is not sufficent evidence to warrant rejection of the claim that the mean weight is less than 14 oz.

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

8) A skeptical paranormal researcher claims that the population of Americans that have seen a UFO, p, is less than 3 in every one thousand.
○ The error of rejecting the hypothesis that the true proportion is 3 in one thousand when it really is 3 in one thousand.
● The error of failing to reject the hypothesis that the true proportion is 3 in one thousand when it is acutally less than 3 in one thousand.
○ The error of rejecting the hypothesis that the true proportion is less than 3 in one thousand when it really is less than 3 in one thousand.

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

Solve the problem

9) Suppose that you wish to use a hypothesis test to test a claim made by a juice bottling company regarding the mean amount of juice in its 16 oz bottles. Why does the orginal claim sometimes become the null hypothesis, and why does it sometimes become the alternative hypothesis? Give an example of a claim which would become the null hypothesis and an example of a claim would become the alternative hypothesis.

The null hypothesis must always contain the condition of equality. If the orginal claim contains equality, it becomes the null hypothesis, if it does not contain equality, it becomes the alternative hypothesis. Examples of claim will be vary. A claim such as “the mean is 16 oz” will become the null hypothesis while a claim such as “the mean is greater than 16 oz” will become alternative hypothesis.

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

10) An aricle in a journal reports that 34% of American fathers take no responsibility for child care. A researcher claims that the figure is higher for father in the town of Littleon. A random sample of 234 fathers from Littleon yielded 97 who did not help with child care. Test the researcher’s claim at the 0.05 significane level.

H0: p = 0.34; H1: p >0.34; Test statistics: z = 2.41; p-value = 0.0080
Critical value: z = 1.645. Reject H0. The sample data support the researcher’s claim that the proportion for the fathers in Littleon is higher than 34%.

11) A poll of 1,068 adult Americans reveals that 48% of the voters surveyed prefer the Democratic candidate for the presidency. At the 0.05 level of significane, test the claim that less than half of all voters prefer the Democrat.

H0: p = 0.5; H1: p < 0.5; Test statistics: z = -1.31; p-value = 0.0951
Critical value: z = -1.645. Fail to reject H0. There is not sufficent sample evidence to support the claim that less than half of all voters prefer the Democrat.

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

Find p-value for the indicated hypothesis test

12) In a sample of 88 children selected randomly from one town, it is found that 8 of them suffer from Asthma. Find the p-value for a test of the claim that the proportion of all children in the town who suffer from Asthma is equal to 11%.
○ 0.2157
○ 0.2843
○ -0.2843
● 0.5686

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) The health of employees is monitored by periodically weighting them. A sample of 54 employees has a mean weight of 183.9 lb. Assuming that \(\sigma \) is known to be 121.2 lb, use a 0.10 significane level to test the claim that the population mean weight of all such employees is less than 200 lb.

H0: \(\mu \) = 200; H1: \(\mu \) < 200. Test statistics, z = -0.98, p-value = 0.1635. Because p-value of 0.1635 is greater than significane level of \(\alpha \) = 0.05, we fail to reject the null hypothesis. There is not sufficent sample evidence to support the claim that the population mean weight is less than 200 pounds.