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Cost-of-living index. Each year, Kiplinger’s complies its
Chapter 7, Problem 125SE(choose chapter or problem)
Cost-of-living index. Each year, Kiplinger’s complies its list of Best Value Cities. One of the statistics used in the rankings is the cost-of-living index, complied by the U.S. Bureau of Labor Statistics. The index measures the cost of living in a city relative to the national average of 100. In 2011, the New York metropolitan area had a cost-of-living index of 218, the highest in the nation. This means that the cost of living in New York City is 118% higher than the average cost of living for the nation. In contrast, Pueblo, Colorado, had the lowest cost-of-living index (84). The table lists the cost-of-living index for each in a sample of seven Southeastern cities.
a. Specify the null and alternative hypotheses for testing whether the true mean cost-of-living index for Southeastern cities differs from the national cost-of-living index of 100.
b. What assumptions about the sample and population must hold in order for the test, part a, to yield valid results?
c. Conduct the hypothesis test using \(\alpha\ =\ .05\).
d. Is the observed significance level of the test greater or less than .05? Justify your answer.
Questions & Answers
QUESTION:
Cost-of-living index. Each year, Kiplinger’s complies its list of Best Value Cities. One of the statistics used in the rankings is the cost-of-living index, complied by the U.S. Bureau of Labor Statistics. The index measures the cost of living in a city relative to the national average of 100. In 2011, the New York metropolitan area had a cost-of-living index of 218, the highest in the nation. This means that the cost of living in New York City is 118% higher than the average cost of living for the nation. In contrast, Pueblo, Colorado, had the lowest cost-of-living index (84). The table lists the cost-of-living index for each in a sample of seven Southeastern cities.
a. Specify the null and alternative hypotheses for testing whether the true mean cost-of-living index for Southeastern cities differs from the national cost-of-living index of 100.
b. What assumptions about the sample and population must hold in order for the test, part a, to yield valid results?
c. Conduct the hypothesis test using \(\alpha\ =\ .05\).
d. Is the observed significance level of the test greater or less than .05? Justify your answer.
ANSWER:Solution
Step 1 of 4
a) We have to specify the null and alternative hypothesis for the test
Here the claim is that the true mean cost of living index for southern cities differ from the national cost of living index of 100
Then the null hypothesis
And the alternative hypothesis