3. the average annual income of 100 randomly chosen residents of santa cruz is $45,221 with a standard deviation of $30,450. a. what is the standard deviation of the mean annual income? b. test the 1-sided hypothesis that the average annual income is $40,000 against the alternative that it is less than $40,000 at the 10% significance level. c. test the 2-sided hypothesis that the average annual income is equal to $42,000 against the alternative that it is not at the 5% significance level. d. what is the confidence interval for part (c)? e. what is the p-value for part (b)? f. do you reject or fail to reject part (c)? write your answer and a complete, accurate, sentence.