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(Solution document) The mean income per person in the United States is $39,000, and the distribution of incomes follows a normal distribution.


The mean income per person in the United States is $39,000, and the distribution of incomes follows a normal distribution. A random sample of 15 residents of Wilmington, Delaware, had a mean of $50,000 with a standard deviation of $9,600. 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?

 

a.State the null hypothesis and the alternate hypothesis.

 

    H0: ? ?    H1: ? >  

 

b.State the decision rule for 0.025 significance level. (Round your answer to 3 decimal places.)

 

  Reject H0 if t > 

 

c.Compute the value of the test statistic. (Round your answer to 3 decimal places.)

 

  Value of the test statistic  

 

d.Is there enough evidence to substantiate that residents of Wilmington, Delaware have more income than the national average at the 0.025 significance level?

 

  

(Click to select)

Reject

Fail to reject

 H0. There is 

(Click to select)

insufficient

sufficient

 evidence to conclude that the mean income in Wilmington is greater than $39,000.

 


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