Question

$2.25	$2.41	$2.30	$2.55	$2.57	$2.65
$2.28	$2.42	$2.32	$2.59	$2.39	$2.64
$2.31	$2.43	$2.49	$2.60	$2.34	$2.79
$2.33	$2.45	$2.51	$2.61	$2.38	$2.59
$2.35	$2.47	$2.53	$2.63	$2.67	$2.73
$2.37	$2.48	$2.54	$2.52	$2.58	$2.56

Assume the alpha value is .05.  Find the mean, standard deviation and confidence interval.

Answer 1

mean=sum(x)/n=89.63/36=2.4897

sd=sqrt(sum((x-mean)²)/n)=sqrt(0.6429/36)=0.1336

here sample size n=36 ( more than 30) so we use z-value to find the confidence interval

(1-alpha)*100% confidence interval for population mean=sample mean±z(alpha/2)*sd/sqrt(n)

95% confidence interval for population mean=sample mean±z(0.05/2)*sd/sqrt(n)=

=2.4897±1.96*0.1336/sqrt(36)=2.4897±0.0436=(2.4463, 2.5333)

n= 36 sample mean= 2.4897 sd= 0.1336 z-value margin of error lower limit upper limit 95% confidence interval 1.96 0.0436 2.4463 2.5333

following information has been generated using ms-excel

s.n.	x	x-2.4897	(x-2.4898)2
1	$2.25	($0.24)	0.05745609
2	$2.28	($0.21)	0.04397409
3	$2.31	($0.18)	0.03229209
4	$2.33	($0.16)	0.02550409
5	$2.35	($0.14)	0.01951609
6	$2.37	($0.12)	0.01432809
7	$2.41	($0.08)	0.00635209
8	$2.42	($0.07)	0.00485809
9	$2.43	($0.06)	0.00356409
10	$2.45	($0.04)	0.00157609
11	$2.47	($0.02)	0.00038809
12	$2.48	($0.01)	9.409E-05
13	$2.30	($0.19)	0.03598609
14	$2.32	($0.17)	0.02879809
15	$2.49	$0.00	9E-08
16	$2.51	$0.02	0.00041209
17	$2.53	$0.04	0.00162409
18	$2.54	$0.05	0.00253009
19	$2.55	$0.06	0.00363609
20	$2.59	$0.10	0.01006009
21	$2.60	$0.11	0.01216609
22	$2.61	$0.12	0.01447209
23	$2.63	$0.14	0.01968409
24	$2.52	$0.03	0.00091809
25	$2.57	$0.08	0.00644809
26	$2.39	($0.10)	0.00994009
27	$2.34	($0.15)	0.02241009
28	$2.38	($0.11)	0.01203409
29	$2.67	$0.18	0.03250809
30	$2.58	$0.09	0.00815409
31	$2.65	$0.16	0.02569609
32	$2.64	$0.15	0.02259009
33	$2.79	$0.30	0.09018009
34	$2.59	$0.10	0.01006009
35	$2.73	$0.24	0.05774409
36	$2.56	$0.07	0.00494209
sum=	$89.6300	$0.0008	$0.6429
n=	$36.0000
mean=	$2.4897
sd=	$0.1336