How many days a year does it rain in Seattle? A local weather person states that the average number of days is 50. Take this as the null hypothesis. The alterntive is that mu does not equal 50. Sigma is 12.

Looking at data from the last nine years, the mean is 55 rainy days per year. What is the 95% confidence interval for x bar? What is the p-value for the null hypothesis? Do you reject the null hypothesis with an alpha level of .o5? Does the hypothesized mu fall within the 95% confidence interval?

What z-score is associated with a 95% confidence interval or .05 alpha level: z(95%)=1.96

What is the standard deviation associated with the sample mean: 12/sqrt(9)=4

What is the 95% confidence interval: 55 plus or minus 4*1.96=7.84

How many z-scores apart is x-bar from the null hypothesis mu:
(55-50)/4=1.25

Is the p-value more or less than the alpha level: more.

To be exact:
plus or minus 1.25 is 79% of the normal distribution, so the p-value is .21