Reference no: EM133042404

Problem 1

Below are the results of a survey of America's best graduate and professional schools. The top 25 business schools, as determined by reputation. student selectivity, placement success, and graduation rate, are listed in the table. For each school. three variables were measured: (1) GMAT score for the typical incoming student: (2) student acceptance rate (percentage accepted of all students who applied): and (3) starting salary of the typical graduating student.

	School	GMAT	Acc. Rate (%)	Salary ($)
1	Harvard	644	15	63,000
2	Stanford	665	10.2	60,000
3	Penn	644	19.4	55,000
4	Northwestern	640	22.6	54,000
5	MIT	650	21.3	57,000
6	Chicago	632	30	55,269
7	Duke	630	18.2	53,300
8	Dartmouth	649	13.4	52,000
9	Virginia	630	23	55,269
10	Michigan	620	32.4	53.3
11	Columbia	635	37.1	52,000
12	Cornell	648	14.9	50,700
13	CMU	630	31.2	52,050
14	UNC	625	15.4	50,800
15	Cal-Berkeley	634	24.7	50,000
16	UCLA	640	20.7	51,494
17	Texas	612	28.1	43,985
18	Indiana	600	29	44,119
19	NYU	610	35	53,161
20	Purdue	595	26.8	43,500
21	USC	610	31.9	49,080
22	Pittsburgh	605	33	43,500
23	Georgetown	617	31.7	45,156
24	Maryland	593	28.1	42,925
25	Rochester	605	35.9	44,499

1- Find the following:
mean & mode of GMAT score.
variance & standard deviation of accepting rate.

2- The academic advisor wants to predict the typical starting salary of a graduate at a top business school using GMAT score of the school as a predictor variable. A simple linear regression of SALARY versus GMAT using the 25 data points in the table are shown above.
a- Find the following po. Apt. S, r2. r. and explain the meaning of each one of them
b- Write the equation of the least square line (between salary & GMAT score)
c- Set up the null and alternative hypotheses for testing whether a positive linear relationship exists between SALARY and GMAT in the situation above.
d- For GMAT = 600 find the prediction interval (95%) of salary and explain the result.

Problem 2
Consider the following set of salary data which compare male & females' income

	Men (1)	Women (2)
Sample Size	100	80
Mean	$12,850	$13,000
Standard Deviation	$345	$500

1- Form the hypothesis to determine if women have a higher mean salary than men.

2- Calculate the appropriate test statistic (Z) to test the hypothesis.

3- At a confidence level 95% test your hypothesis.

4- Choose an industry in your country and gather similar data, then Form the hypothesis to determine if men have a higher mean salary than women (in your country) explain and evaluate the results and make suggestions to reach equality.