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Activity 6

Activity 6—MATH 250
Elements of Statistics—Fall 2015 MATH 250- Elements of Statistics
DUE DATE:  11/10/2015 Class Data, Fall 2015---CLEANED Student Data
NAME: Individual# Gender Foot Length (cm) Height (cm) Armspan (cm) Age (years) Number in Family Hair Color
1 Female 25.4 170.18 170.2 43 5 Brown
General Instructions: Please place your name above, then complete the following questions. NOTE: Read the entire document below to get a feel for the activity before continuing. Make sure to save this Excel file often using the filename "yournameActivity6". Once complete, submit your answers to this activity by attaching your Excel file through the completion link in the Unit 3 Activity 6 assignment description in Blackboard. Use the area to the near right in this Excel worksheet when calculating any statistics/parameters. Methods/work used to calculate values and reach conclusions must be shown in the spreadsheet in order to receive full credit. 2 Female 22 160.02 162.6 39 12 Brown
3 Female 18.5 139.5 162 29 3 Brown
4 Female 26 176.5 178 41 9 Blonde
5 Male 25.5 181 179.5 29 9 Brown
6 Female 24 162.5 148 21 4 Brown
7 Male 28 173 182 39 6 Brown
8 Female 23.5 161 158 32 4 Blonde
9 Female 23 161 154 25 3 Brown
Overview: 10 Female 26 156 152 31 6 Red
As discussed in the 8th Chapter of your text, one can use data from a random sample to test a claim or hypothesis about a population. For example one might want to test the claim that the mean age of all FHSU Elements of statistics students is at least 30 years. In this activity, you will apply your understanding of hypothesis testing to actual data—the data collected in Activity 1a of this course. This activity is designed to have you use the cleaned class data from Activity 4 to test some claims. This data is given again to the right. 11 Female 26 173 173 18 4 Brown
12 Female 24 161.5 160 24 7 Blonde
13 Male 26.5 185 188 24 5 Brown
14 Female 25 165 172.5 36 4 Blonde
15 Female 25.5 170 170 33 4 Brown
16 Female 23 161.5 166.5 20 4 Brown
17 Female 24 170 164 46 5 Brown
NOTE: In all three of these problems below, you are required to demonstrate your analysis process as described in the text, not just the final conclusion. Also, as stated in the resources, there are requirements to applying hypothesis testing that should be checked--requirements that our collected data will actually fail to meet (for instance, the sample should be randomly selected from the population of interest). However, for simplicity of the activity you MAY ASSUME that all requirements for hypothesis testing have been met in regard to the data collection process. 18 Female 22 135 148 31 4 Brown
19 Male 28 173 188 29 4 Brown
20 Female 23 167.5 150 25 3 Brown
21 Female 23.5 165 157 30 5 Brown
22 Female 25.5 175 170 37 5 Blonde
23 Female 22.5 157.5 148.5 28 6 Brown
24 Male 25 173 176 25 7 Blonde
25 Male 25 172.5 161 20 4 Black
1. Past enrollment data indicates that 20% of the students taking elementary statistics at FHSU have a family size of four people. Is the enrollment in this semester's virtual classes significantly more than this claim, as measured statistically? Justify your answer through a formal hypothesis testing procedure on proportions with a 5% level of significance. It is required that you give needed hypotheses and related statistical values below as well as statistical computations to the right (feel free to use the appropriate template from the Excel guide for Unit 3). Then give a proper final interpretive conclusion below based on the statistical measures calculated and related to the context given. 26 Female 24.5 162.5 164.5 34 5 Brown
27 Male 25 178 181 19 5 Brown
28 Female 23.5 157.5 160 22 2 Brown
29 Female 20 159 160 22 4 Brown
30 Female 21.5 163.5 162 26 3 Brown
31 Female 22 152 150 20 3 Brown
32 Male 28.5 187.5 185.5 24 4 Blonde
H0: 33 Male 24 174 155 44 1 Brown
H1: 34 Female 24 169 178 27 3 Brown
Sample proportion (p-hat): 35 Female 24.00 171 162 26 5 Brown
Critical Value: 36 Female 20.9 166 169 23 3 Blonde
Sample's Test Statistic: 37 Female 24.5 165 167.5 29 5 Brown
P-value: 38 Female 51 170 167.5 28 3 Brown
CONCLUSION: 39 Female 25 156 151 55 4 Brown
40 Female 23.5 157 153 41 3 Blonde
41 Male 24 174 174 41 1 Red
42 Female 25.5 162 166.5 30 9 Brown
43 Female 25.5 171 171 28 2 Blonde
44 Male 28 183 187.5 37 4 Red
45 Female 24 173.5 167.5 27 5 Blonde
46 Female 24 170.5 170 20 5 Brown
47 Male 33 192 183 26 5 Brown
48 Female 23.5 159 161.9 44 3 Brown
49 Female 23 157.5 154.5 30 10 Brown
50 Female 25.5 170 179 41 4 Brown
51 Female 26 165 164.5 52 5 Black
2. It has been claimed that the mean age of all FHSU Virtual College statistics students is 28.65 years old. Using the age data collected from this summer's classes, test this hypothesis--that is does the collected data statistically support this claim or is the mean age likely different from 28.65 years old? Justify your answer through a formal hypothesis testing procedure with a 0.10 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.) 52 Female 24.5 165 162.5 38 11 Blonde
53 Female 24 173 164 48 1 Blond
55 Female 24 162.5 168 50 24 Red
56 Male 18.5 180 143 21 3 Black
57 Male 28 183.5 183 23 5 Brown
58 Male 28 180 177 30 5 Brown
59 Female 23 169 154 31 6 Red
H0: 60 Female 24.5 160.5 159 19 9 Brown
H1: 61 Female 19 152.5 152.5 33 5 Black
Sample's Mean (x-bar): 62 Female 21.5 161.5 159.5 31 2 Brown
Sample's S.D. (s): 63 Female 25 170.5 174 25 2 Blonde
Critical Value: 64 Female 24 160 152 24 7 Blonde
Sample's Test Statistic: 65 Male 29 180 179 25 3 Brown
P-value: 66 Female 24 170 178 20 5 Red
CONCLUSION: 67 Female 24.5 171.5 161 29 3 Brown
68 Female 27 180.5 173.5 45 4 Brown
69 Female 23.5 157 153 41 3 Blonde
70 Female 23 162.5 160 33 4 Brown
71 Female 25.5 183 173 28 4 Blonde
72 Female 23.5 174 155 39 4 Brown
73 Female 26 176 177 26 6 Brown
74 Male 27.9 182.9 188 24 3 Red
75 Female 24 175.5 170 30 3 Blonde
76 Male 25.5 185.5 190 24 3 Brown
3. It has been claimed that the mean armspan of adults in the US is greater than 162.5 cm. Does the data of our statistics 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.
H0:
H1:
Sample's Mean (x-bar):
Sample's S.D. (s):
Sample's Test Statistic:
P-value:
CONCLUSION: