The mean income per person in the United States is $39,500, and the distribution of incomes follows a normal distribution. A random sample of 16 residents of Wilmington, Delaware, had a mean of $45,500 with a standard deviation of $9,800. At the 0.010 level of significance, is that enough evidence to conclude that residents of Wilmington, Delaware, have more income than the national average?
To test null hypothesis against alternative hypothesis
sample standard deviation
and sample size
The test statistic can be written as
which under H0 follows a t distribution with n-1 df.
We reject H0 at 0.01 level of significance if P-value < 0.01
The value of the test statistic =
and P-value =
Since P-value < 0.01, so we reject H0 at 0.01 level of significance and we can conclude that there is enough evidence to substantiate that residents of Wilmington, Delaware, have more income than the national average.
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