Confidence interval for the average height of year

Question

Discuss the below:

Q: A US Navy recruiting center knows from past experience that the height of its recruits are normally distributed with mean 68 inches. The recruiting center wants to test the claim that the average height of this year's recruits is greater than 68 inches. To do this, recruiting personnel take a random sample of 64 recruits from this year and record their heights (in inches).

a. On the basis of the available sample information, do the recruiters find support for the given claim at the 1% significance level? Explain.

b. Use the sample data to construct a 95% confidence interval for the average height of this year's recruits. Based of this confidence interval, what conclusion should recruiting personnel reach regarding the given claim?

Heights of Randomly Selected Navy Recruits
Recruit	Height
1	71.51
2	71.00
3	71.60
4	66.76
5	72.97
6	69.32
7	63.03
8	67.62
9	68.92
10	68.42
11	67.59
12	70.94
13	66.27
14	72.33
15	68.54
16	62.52
17	57.54
18	68.93
19	67.68
20	67.60
21	70.35
22	69.06
23	66.32
24	71.73
25	65.46
26	67.46
27	66.95
28	66.87
29	68.74
30	69.95
31	65.83
32	72.02
33	64.49
34	68.26
35	66.50
36	62.32
37	71.78
38	67.51
39	68.54
40	64.61
41	66.14
42	69.07
43	69.81
44	65.25
45	68.83
46	64.11
47	69.28
48	67.70
49	67.43
50	66.12
51	67.80
52	68.57
53	70.55
54	61.80
55	65.45
56	65.48
57	71.31
58	63.48
59	71.75
60	71.10
61	68.61
62	63.31
63	64.13
64	68.66