Please show work According to state government the monthly i

Please show work

According to state government, the monthly incomes of college graduates have a standard deviation of $675. A county official believes that the standard deviation of monthly incomes is higher in her county.

A sample of 71 college graduates are randomly selected and found to have a standard deviation of $705. Assuming the distribution of incomes of college graduates is normally distributed, test the claim using the P-value approach with ? = 0.05.

Solution

Let o be the standard deviation

The test hypothesis:

Ho: o=675 (i.e. null hypothesis)

Ha: o >675 (i.e. alternative hypothesis)

The test statistic is

chisquare =(n-1)*s^2/o^2

=(71-1)*705^2/675^2

=76.36

The degree of freedom =n-1=71-1=70

It is a right-tailed test.

The p-value= P(X^2 with df=70 >76.36) =0.2816 (from chisquare table)

Since the p-value is larger than 0.05, we do not reject the null hypothesis.

So we can not conclude that the standard deviation of monthly incomes is higher in her county.