Question

Estimate the population mean μ in two ways. (a) Give a point estimate for μ and a “margin of error”. (b) Construct a 99% confidence interval for μ (c) Approximately what kind of distribution does the random variable (x bar) have, and why? What is the name of the theorem that tells you so? Below is sample data:
7.13
6.5
6.4
6.53
6.58
6.63
7.11
7.04
7
7.15
6.76
6.96
7.14
7.21
7.25
7.18
7.12
6.55
7.18
7.05
6.59
6.88
6.94
6.85
6.59
6.6
6.98
6.68
7.07
7.21
6.88
7.01
7.02
6.69
6.9
6.76
6.3
6.64
6.81
6.87
6.97
6.62
7.03
6.61
6.99
6.6
6.86
7.1
6.79
7.02
6.89
6.83
6.97
6.76 I calculated the mean is 6.8662 and standard dev. is 0.232, and sample size is 54

Answer 1

sr.no.	x	x-x̅	(x-x̅)^2
1	7.13	0.2637	0.0695
2	6.5	-0.3663	0.1342
3	6.4	-0.4663	0.2174
4	6.53	-0.3363	0.1131
5	6.58	-0.2863	0.0820
6	6.63	-0.2363	0.0558
7	7.11	0.2437	0.0594
8	7.04	0.1737	0.0302
9	7	0.1337	0.0179
10	7.15	0.2837	0.0805
11	6.76	-0.1063	0.0113
12	6.96	0.0937	0.0088
13	7.14	0.2737	0.0749
14	7.21	0.3437	0.1181
15	7.25	0.3837	0.1472
16	7.18	0.3137	0.0984
17	7.12	0.2537	0.0644
18	6.55	-0.3163	0.1000
19	7.18	0.3137	0.0984
20	7.05	0.1837	0.0337
21	6.59	-0.2763	0.0763
22	6.88	0.0137	0.0002
23	6.94	0.0737	0.0054
24	6.85	-0.0163	0.0003
25	6.59	-0.2763	0.0763
26	6.6	-0.2663	0.0709
27	6.98	0.1137	0.0129
28	6.68	-0.1863	0.0347
29	7.07	0.2037	0.0415
30	7.21	0.3437	0.1181
31	6.88	0.0137	0.0002
32	7.01	0.1437	0.0207
33	7.02	0.1537	0.0236
34	6.69	-0.1763	0.0311
35	6.9	0.0337	0.0011
36	6.76	-0.1063	0.0113
37	6.3	-0.5663	0.3207
38	6.64	-0.2263	0.0512
39	6.81	-0.0563	0.0032
40	6.87	0.0037	0.0000
41	6.97	0.1037	0.0108
42	6.62	-0.2463	0.0607
43	7.03	0.1637	0.0268
44	6.61	-0.2563	0.0657
45	6.99	0.1237	0.0153
46	6.6	-0.2663	0.0709
47	6.86	-0.0063	0.0000
48	7.1	0.2337	0.0546
49	6.79	-0.0763	0.0058
50	7.02	0.1537	0.0236
51	6.89	0.0237	0.0006
52	6.83	-0.0363	0.0013
53	6.97	0.1037	0.0108
54	6.76	-0.1063	0.0113
Total	370.78		2.8733
mean=x̅	Total/54
x̅=	6.8663