Test of hypothesis

1) It has been claimed that the mean age of all FHSU Virtual College statistics students is at most 30 years old. Using the age data collected from this class, test this hypothesis--that is does the data set of our class statistically support this claim or is the mean age value likely higher? Justify your answer through a formal hypothesis testing procedure with a 0.05 level of significance. Again, necessary claims, calculations, and values must be shown below and to the right. Give your proper/final conclusion below. (Hint: Since the population s.d. is not known, make sure to realize the need to use the t-distribution for testing purposes.)

2) It has been claimed that the average family size in the US is 2.60 people? Does the data set of our class support or contradict this claim? Justify your answer through a formal hypothesis testing procedure with a P-value approach using a significance level of your choice. Calculation of and interpretation of the P-value is required on this problem. Give your final conclusion below.

Data:
Individual# Gender Foot Length Height Age Armspan Number in Family Hair Color
1 M 25 176 31 172 3 brown
2 F 23 158.5 35 157 4 brown
3 F 23 162 40 161 2 blonde
4 F 23 162 24 158 2 brown
5 F 20 165 24 159 4 brown
6 M 28 178 26 175 3 blonde
7 F 24 172.5 32 166 4 blonde
8 F 24 174 35 169 5 brown
9 M 26.5 188 30 190 7 brown
10 F 23 157.5 32 152.5 3 brown
11 F 20 158.5 46 155 3 blonde
12 F 23.5 163 27 164 4 brown
13 F 25 163 55 162 2 brown
14 F 24 166 37 165 6 brown
15 F 22 173.5 27 174.5 4 blonde
16 F 25.5 161.5 34 160 2 brown
17 F 23 178 26 178 3 brown
18 M 27.5 182 26 180 2 brown
19 F 24 164 36 164 5 brown
20 F 23 166 29 160 3 black
21 F 25.5 160 47 164 6 brown
22 F 23 156 33 154 5 brown
23 M 27 183 25 180 5 black
24 F 23.5 170 25 165 4 brown
25 F 22 173.5 27 174 5 blonde
26 M 28 177 20 180 4 brown
27 F 25 156 55 155 1 red
28 F 21 155 45 157 8 auburn
29 M 24.5 185 32 182 4 brown
30 M 29 183 23 205.5 4 brown
31 M 30.5 185 24 180 5 brown
32 F 27 169 28 164 6 blonde
33 F 24 158 26 161 5 brown
34 F 22 162.5 24 161.5 4 brown
35 F 22 168 34 171 5 brown
36 F 23 168.5 30 166.5 4 brown
37 F 24 165 34 160 5 brown
38 F 23 170.5 22 170.18 2 brown
39 F 22 161 27 159 3 lt. brown
40 F 23.5 170 27 170 6 blonde
41 F 22.5 168 41 166 4 brown
42 F 24.5 163 51 177.5 3 brown
43 F 23 165 26 162 3 strawberry blonde
44 F 24 167 21 171 4 brown
45 F 25.5 178 30 174 3 brown
46 F 23 157 46 151 5 brown
47 F 17.5 124 25 124 4 brown
48 M 27.5 180 58 177 2 grey/brown
49 F 24 157 36 160 5 red/brown
50 F 23 156.5 28 151 1 blonde

Please see attachment;