The mean income per person in the United States is 41000 and

The mean income per person in the United States is $41,000, and the distribution of incomes follows a normal distribution. A random sample of 9 residents of Wilmington, Delaware, had a mean of $51,000 with a standard deviation of $10,400. At the 0.025 level of significance, is that enough evidence to conclude that residents of Wilmington, Delaware, have more income than the national average?

Solution

State the decision rule for 0.025 significance level.

The degree of freedom =n-1=9-1=8

Given a=0.025, the critical value is t(0.025, df=8) =2.306 (from student t table)

Reject H₀ if t > 2.31

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Compute the value of the test statistic.

The test statistic is

t=(xbar-mu)/(s/vn)

=(51000-41000)/(10400/sqrt(9))

=2.885