Question

The average per capita income for Wisconsin is reported to be 37,314, and for South Dakota it is37,375 - almost the same thing. A random sample of 50 workers from each state indicated the following sample statistics for South Dakota: mean = 10,500, standard deviation =12,500. At a significance level of 0.05, can we conclude a difference in means of the personal incomes?

Answer 1

To determine if there is a significant difference in means of personal incomes between Wisconsin and South Dakota, we need to perform a hypothesis test. However, without the necessary sample statistics for Wisconsin, we cannot conclude the existence of a difference in means.

Step-by-step explanation:

To answer the question, we need to perform a hypothesis test to determine if there is a significant difference in means. We can use a two-sample t-test since we have two independent samples from different populations. The null hypothesis (H0) states that there is no difference in means, and the alternative hypothesis (Ha) states that there is a difference in means. We will compare the test statistic (t-value) to the critical value from the t-distribution table at a significance level of 0.05.

Given the sample statistics for South Dakota, we have a sample mean of $10,500 and a standard deviation of $12,500. However, we do not have the sample mean or standard deviation for Wisconsin. Without the necessary information for Wisconsin, we cannot perform the hypothesis test.

In conclusion, we cannot determine if there is a significant difference in means of personal incomes between Wisconsin and South Dakota without the sample statistics for Wisconsin.