Question

4a) Build a 95% confidence interval for the average salary that a financial advisor in California can expect to make. Make sure to check all conditions and interpet your interval. What percent of the individuals in your sample fall in this interval? Does this contradict the 95% confidence level? Why or why not?

4b) Carry out a hypothesis test at α = .05 to see if the average salary for male financial ad- visors in California is different from the average salary for female financial advisors in California. Make sure to check all necessary conditions and state your conclusion in the context of this situation.

4c) Construct a 95% confidence interval for the average difference in salary between male and female financial advisors in California. Make sure to interpet your interval.

4d) Disparity on wages based on gender is obviously a serious issue and parts 4b and 4c indi- cate that this may be happening in our data set. However, recall that from Part 2 of this project another important variable was years of experience. What was the average years of experience for males in our data set? What was the average years of experience for females in our data set? How might this explain what you found in 4b and 4c?

respondent	years of experience	degree	gender	salary (in thousands)	satisfaction rating(1-10)
4	1	Business	female	70	6
1	2	Business	female	65	1
10	2	Math	male	74	5
7	3	Business	female	74	4
13	3	Economics	female	77	7
19	3	Business	female	82	8
20	3	Economics	male	82	7
16	4	Business	female	80	5
5	4	Economics	female	86	9
2	5	Economics	female	85	5
14	5	Math	male	90	10
17	6	Math	female	93	9
8	6	Business	male	86	5
11	7	Business	female	88	4
25	8	Economics	female	95	6
21	8	Economics	male	93	5
23	9	Business	male	94	2
24	9	Economics	male	98	4
26	10	Business	male	97	5
3	10	Math	male	105	6
22	12	Math	male	102	5
9	12	Business	male	108	6
6	13	Economics	female	107	5
12	13	Economics	male	114	7
15	13	Math	male	116	8
18	14	Economics	male	124	10

Answer 1

4a. We have to make a 95% confidence interval for the average salary that a financial advisor in California is expected to make.

respondent(fi)	years of experience	degree	gender	salary(xi)	satisfaction rating	total wage
4	1	business	female	70	6	280	584.6724	2338.69
1	2	business	female	65	1	65	851.4724	851.4724
10	2	math	male	74	5	740	407.2324	4072.324
7	3	business	female	74	4	518	407.2324	2850.627
13	3	economics	female	77	7	1001	295.1524	3836.981
19	3	business	female	82	8	1558	148.3524	2818.696
20	3	economics	male	82	7	1640	148.3524	2967.048
16	4	business	female	80	5	1280	201.0724	3217.158
5	4	economics	female	86	9	430	66.9124	334.562
2	5	economics	female	85	5	170	84.2724	168.5448
14	5	math	male	90	10	1260	17.4724	244.6136
17	6	math	female	93	9	1581	1.3924	23.6708
8	6	business	male	86	5	688	66.9124	535.2992
11	7	business	female	88	4	968	38.1924	420.1164
25	8	economics	female	95	6	2375	0.6724	16.81
21	8	economics	male	93	5	1953	1.3924	29.2404
23	9	business	male	94	2	2162	0.0324	0.7452
24	9	economics	male	98	4	2352	14.5924	350.2176
26	10	business	male	97	5	2522	7.9524	206.7624
3	10	math	male	105	6	315	117.0724	351.2172
22	12	math	male	102	5	2244	61.1524	1345.353
9	12	business	male	108	6	972	190.9924	1718.932
6	13	economics	female	107	5	642	164.3524	986.1144
12	13	economics	male	114	7	1368	392.8324	4713.989
15	13	math	male	116	8	1740	476.1124	7141.686
18	14	economics	male	124	10	2232	889.2324	16006.18
351						33056		57547.05	Total

mean =

variance=

Thus, the mean == 33056/351=94.18

and the variance = = 57547.05/351=163.95

the CI is given by

n=351

here and, the value of

thus putting the values, we have the 95% confidence interval as (92.84,95.52)

The values lying in the confidence interval is = 17+25+24+23=86

The percentage of values lying in the confidence interval is (86/351)*100=24.5

A 95% confidence interval is a range of values that you can be 95% certain contains the true mean of the population. This is not the same as a range that contains 95% of the values.The 95% confidence interval defines a range of values that you can be 95% certain contains the population mean.