Problem 8: One Of The Most Difficult Things To Do In Statist

Problem 8one Of The Most Difficult Things To Do In Statistics Is To De

Determine the most appropriate hypothesis test to use for the following scenario: Each year, Kiplinger’s compiles its list of Best Value Cities. One of the statistics used in this ranking is the cost-of-living index compiled by the US Department of Labor Bureau of Labor Statistics. The index measures the cost of living in a city relative to the national average of 100. In 2011, Pueblo Colorado had the lowest index (84), while New York City had an index of 118.

The following table lists the cost of living for seven Southeastern US cities:

• Charlotte, NC: 93.0
• Birmingham, AL: 89.6
• Florence, SC: 100.0
• Tampa, FL: 92.1
• Atlanta, GA: 95.2
• Knoxville, TN: 89.7
• Miami, FL: 107.7

Is the true mean cost of living index for Southeastern US cities lower than the national mean cost-of-living index of 100? Test at 2% significance level. The most appropriate hypothesis test to use for this scenario is:

Paper For Above instruction

In determining the appropriate hypothesis test for this scenario, it is essential to analyze the nature of the data and the research question. The goal is to assess whether the average cost of living index for Southeastern U.S. cities is statistically lower than the national average of 100. The data consist of a sample of seven cities with their respective cost of living indices, which are continuous variables. Since the population standard deviation is unknown and the sample size is small, a t-test for a single sample is suitable for this analysis.

Specifically, a one-sample t-test will compare the sample mean of the Southeastern cities’ cost of living indices against the known population mean of 100. The null hypothesis (H0) posits that the mean cost of living in Southeastern cities equals the national average, while the alternative hypothesis (Ha) suggests that the mean is less than 100. Mathematically, these hypotheses are expressed as:

• H0: μ = 100
• Ha: μ

This test is appropriate because it evaluates whether a small, non-random sample's mean significantly deviates from a hypothesized population mean, considering the added uncertainty due to small sample size and unknown population standard deviation. The significance level of 0.02 (2%) signifies that if the p-value from the test is less than 0.02, we reject the null hypothesis, providing evidence that the true mean cost of living in Southeastern cities is lower than the national average.

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