Question

Construct a 95% confidence interval for the average difference between the job satisfaction of a lawyer and a cabinet maker.

Lawyer	Physical Therapist	Cabinetmaker	Systems Analyst
44	55	54	44
42	78	65	73
74	80	79	71
42	86	69	60
53	60	79	64
50	59	64	66
45	62	59	41
48	52	78	55
64	55	84	76
38	50	60	62

Answer 1

To estimate the confidence interval

First we need to estimate the mean and standard deviation

For lawyer

Mean (u1)= 50

S.d(s1) = 11.1455

For cabinet maker

Mean(u2) = 69.1

S.d (s2)= 10.2897

N1 = N2 = sample size = 10

Point estimate = D = u1-u2 = -19.1

Degrees of freedom is smaller of n1-1, n2-1

Df is 9 in this case

For df 9 and 95% confidence level, t = 2.262

Margin of error = MOE = t*standard error

Standard error = √{(s1^2/n1)+(s2^2/n2)}

After substituting all the values

MOE = 10.850531218965

Confidence interval is given by,

(D-MOE, D+MOE)

(−29.95053121896, −8.249468781034)