1. In an attempt to compare the starting salaries of university graduates majoring in education and social sciences, random samples of 50 recent university graduates in each major were selected and the following information was obtained:

Major Mean SD

Education ($) $40,554 2225

Social science ($) $38,348 2375

(a) Find a point estimate for the difference in the average starting salaries of university students majoring in education and the social sciences. What is the margin of error for your estimate?

(b) Based on the results of part a, do you think that there is a significant difference in the means for the two groups in the general population? Explain.

please show work

2. It is a well-accepted fact that males are taller on average than females. But how much taller? The heights and genders of 105 biomedical students were recorded and the data are summarized below:

Males Females

Sample size 48 77 Sample mean (cm) 176.7 163.7

Sample standard deviation 6.7 6.6

a)Performatestofhypothesistoeitherconfirmorrefuteourinitialclaimthatmalesaretalleronaveragethanfemales.Use alpha =0.01.

b) If the results of part a show that our claim was correct, construct a 99% confidence one- sided lower confidence bound for the average difference in heights between male and female students. How much taller are males than females?

Please show work