Question

1. Assume student working hours are normally distributed. A random sample of 21 employed Green River students were asked how many hours per week they work. The results are in the table below.

48, 40, 25, 40, 40, 13, 24, 38, 24, 40, 50, 45, 10, 40, 40, 10, 16, 25, 40, 18, 45

Find the 95% confidence interval for the population mean, rounded to the nearest whole number. Interpret your result.

Answer 1

Solution :

Given that,

x	x2
48	2304
40	1600
25	625
40	1600
40	1600
13	169
24	576
38	1444
24	576
40	1600
50	2500
45	2025
10	100
40	1600
40	1600
10	100
16	256
25	625
40	1600
18	324
45	2025
∑x=671	∑x2=24849

Mean ˉx=∑xn

=48+40+25+40+40+13+24+38+24+40+50+45+10+40+40+10+16+25+40+18+45/21

=671/21

=31.9524

Sample Standard deviation S=√∑x2-(∑x)2nn-1

=√24849-(671)221/20

=√24849-21440.0476/20

=√3408.9524/20

=√170.4476

=13.0556

Degrees of freedom = df = n - 1 = 21 - 1 = 20

At 95% confidence level the t is ,

  = 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t /2,df = t0.025,20 =2.086

Margin of error = E = t/2,df * (s /n)

= 2.086 * (13.06 / 21)

= 5.94

Margin of error = 5.94

The 95% confidence interval estimate of the population mean is,

- E < < + E

31.95 - 5.94 < < 31.95 + 5.94

26.00 < < 37.89

(26.00, 37.89 )