Activity 6—MATH 250

Elements of Statistics—Fall 2021 MATH 250- Elements of Statistics

DUE DATE: 11/10/2021 Class Data, Fall 2021—CLEANED Student Data (Renumbered 1-98)

Assessment /25 NAME: Individual ID# Gender Foot Length Height Age Armspan Number in Family Hair Color

1 Female 25.5 145.0 34 143.0 4 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 24.5 180.0 41 184.5 4 Red

3 Female 23.5 161.5 29 161.5 3 Brown

4 Female 24.5 160.0 48 161.5 8 Brown

5 Female 24.0 170.0 36 172.0 5 Brown

6 Male 27.0 183.0 27 182.0 4 Brown

7 Female 25.5 174.0 45 171.5 3 Brown

8 Male 26.5 172.5 21 172.5 5 Red

9 Female 25.5 142.0 23 142.0 5 Brown

Overview: 10 Male 26.5 180.0 23 180.0 4 Brown

As discussed in the 11th & 12th chapters of the 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 Online students is over thirty 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 of 98 data values in each variable to test some claims. This data is given again to the right, and you are encouraged to use the templates given in the Unit 3, Part 1 Excel Guide. When you use a template, copy & paste the entire template (including the title) to the right of the problem, then make changes to the values or calculations in the template, and this will serve as your “work” for that particular problem. For specific directions about the templates, see the blue box below and to the right. 11 Male 25.0 172.5 51 179.0 10 Brown

12 Male 23.0 182.5 21 180.0 3 Black

13 Female 22.5 159.0 29 160.0 9 Blonde

14 Male 25.5 168.0 28 166.5 5 Brown

15 Female 23.0 159.0 33 157.5 4 Brown

16 Female 23.0 160.0 23 156.0 3 Brown

17 Male 26.0 179.0 41 184.0 5 Brown

18 Male 28.0 189.0 28 187.0 4 Brown

19 Female 23.0 162.5 37 163.0 6 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 regarding the data collection process. Again, don’t forget that the Unit 3 Excel Guide (part 1) includes templates that one should use to produce key testing measures quickly. 20 Female 23.0 181.0 24 174.0 7 Red

21 Female 20.0 160.0 20 160.0 5 Brown

22 Female 22.0 157.5 34 162.0 2 Brown

23 Female 23.5 169.0 27 169.0 5 Red

24 Male 26.0 173.0 22 170.0 4 Brown

25 Female 24.0 162.5 27 164.5 4 Blonde

“To use the templates correctly:

1. Based on the claim in the problem, highlight the correct template you need including the title and select control-c to copy.

2. Go back to the right of the problem you are working and paste the template using control-v.

3. Enter or calculate the values related to the variables in red. If the template asks for x-bar or s, calculate those values using Excel commands within the template. DO NOT ENTER ROUNDED VALUES INTO THE TEMPLATE.

4. Draw proper conclusions based upon the resulting calculated values.” 26 Female 26.5 152.5 38 157.5 7 Brown

27 Female 23.0 163.0 32 165.0 2 Brown

1. “It has been claimed that the mean age of all FHSU Online Elements of Statistics students is more than thirty years old. Using the “”Age”” sample data collected from this year’s classes, test this hypothesis–that is, does the collected data statistically support or contradict this claim? Justify your answer through a formal hypothesis testing procedure with a 0.05 (5%) level of significance. Carefully follow the directions below.

After typing out a) and b) below, use scratch paper to identify all variables from the given information using the correct symbols (s, σ, µ, x-bar, n, p, α, etc.), then go to the templates tab in the Unit 3 Excel Guide (part 1) and determine which template to use, based on the claim in the problem. Copy and paste the entire template (including title) to the right of the problem using the instructions in the blue-shaded area. Use cell references from the completed template to answer parts c) – g). Do not round the values.

Next, give the conclusion of your hypothesis test (choose “”reject the null hypothesis”” or “”fail to reject the null hypothesis””) based on the test statistic and the p-value and explain why you chose your conclusion.

Finally, give an interpretive sentence. Follow examples given in the Unit 3 Excel Guide for correct wording.” 28 Female 25.0 167.5 32 165.0 3 Brown question 1

29 Female 24.5 157.5 26 155.0 3 Brown mean 29.10204082

30 Female 25.5 171.0 37 167.5 12 Blonde stand.deviation 8.336344221

31 Female 21.5 157.5 34 158.0 5 Brown x 97

32 Female 25.5 165.0 19 169.0 7 Brown

33 Female 25.5 170.0 24 168.0 4 Purple

34 Female 21.0 167.0 24 167.0 4 Black

35 Female 24.0 170.0 20 170.0 3 Blonde

36 Male 29.5 188.0 34 189.5 4 Blonde

37 Female 25.0 177.0 41 173.0 5 Blonde

38 Male 30.0 185.5 31 185.5 1 Black

39 Male 26.5 179.5 31 177.5 3 Brown

40 Female 25.0 170.0 45 168.0 3 Blonde

PROVIDE THE FOLLOWING INFORMATION. FOR EACH STATISTIC, USE A CELL REFERENCE FROM YOUR TEMPLATE: 41 Male 28.0 187.0 21 188.0 7 Black

a) H0: µ≤31 42 Female 23.0 163.0 28 164.0 3 Red

b) H1: µ>31 43 Male 24.5 181.0 38 183.0 4 Brown

c) Sample’s Mean (x-bar): 29 44 Female 23.5 166.5 29 169.5 2 Brown

d) Sample’s S.D. (s): 8.7 45 Male 24.5 178.0 34 176.5 2 Brown

e) Critical Value: -4.904 46 Female 24.0 167.0 18 167.0 3 Brown

f) Sample’s Test Statistic: 1.661 47 Female 24.0 186.0 50 183.5 4 Brown

g) P-value: 1 48 Female 25.5 171.5 24 171.0 5 Brown

CONCLUSION OF HYPOTHESIS TEST BASED ON TEST STATISTIC AND P-VALUE AND EXPLAIN WHY: 49 Female 25.0 181.5 25 179.5 6 Black

using the p -value approch the p-value is =1 and since p=1 whivh is greater than 0.05 so we conclide that the null hypothis is not rejected 50 Male 25.5 177.5 39 175.0 4 Black

51 Female 25.0 169.0 19 170.0 3 Red

52 Female 24.0 172.5 22 173.5 2 Blonde

FINAL INTERPRETIVE SENTENCE: 53 Male 29.0 188.0 29 196.0 4 Brown

it is colcluded that the null hypothesis ho is not rejected therefore there is not enough evidence to claim that the population mean is greater than 31 at the 0.05 significant level. 54 Male 26.5 169.0 25 172.0 5 Brown

55 Female 24.0 160.0 25 160.0 6 Brown

56 Female 26.0 170.0 37 168.0 6 Blonde

57 Female 22.5 155.0 27 153.0 4 Brown

58 Female 23.0 155.0 20 157.5 4 Brown

59 Female 24.0 162.5 23 160.0 6 Black

60 Female 23.0 170.0 21 171.0 5 Blonde

61 Male 28.0 183.0 28 180.0 4 Brown

2. “Past enrollment data indicates that 58% of the students taking Elements of Statistics online at FHSU come from families of size four or larger. Is the enrollment in this semester’s online class significantly different from this claim, as measured statistically? Justify your answer through a formal hypothesis testing procedure with a 1% level of significance.

After typing out a) and b) below, use scratch paper to identify all variables from the given information using the correct symbols (s, σ, µ, x-bar, n, p, α, etc.), then go to the templates tab in the Unit 3 Excel Guide (part 1) and determine which template to use, based on the claim in the problem. Copy and paste the entire template (including title) to the right of the problem using the instructions in the blue-shaded area above. Use cell references from the completed template to answer parts c) – g).

Next, give the conclusion of your hypothesis test (choose “”reject the null hypothesis”” or “”fail to reject the null hypothesis””) based on the test statistic and the p-value and explain why you chose your conclusion.

Finally, give an interpretive sentence. Follow examples given in the Unit 3 Excel Guide for correct wording.” 62 Female 23.0 154.0 33 154.0 4 Brown

63 Male 27.0 172.5 18 173.0 7 Brown

64 Female 20.0 160.0 31 165.0 5 Blonde

65 Male 26.5 172.5 21 175.5 5 Brown

66 Female 23.0 159.0 19 160.0 4 Brown

67 Male 25.0 168.0 25 170.0 3 Black

68 Male 28.0 170.5 36 178.0 2 Black

69 Female 22.0 160.0 49 156.0 8 Red

70 Female 28.5 161.5 41 157.0 2 Blonde

71 Male 26.0 175.0 20 179.5 4 Brown

72 Female 23.0 156.0 22 160.0 3 Blonde

73 Male 25.0 175.0 27 177.0 4 Brown

74 Male 27.5 184.0 18 191.5 4 Blonde

PROVIDE THE FOLLOWING INFORMATION. FOR EACH STATISTIC, USE A CELL REFERENCE FROM YOUR TEMPLATE: 75 Female 23.0 161.0 25 165.0 8 Blonde

a) H0: p=0.58 76 Female 24.0 160.0 27 158.0 4 Brown

b) H1: p≠0.58 77 Female 25.5 164.0 25 172.5 11 Brown

c) Sample proportion (p-hat): 0.714285714 78 Male 26.0 178.0 48 180.0 4 Brown

d) Critical Value: 2.575829304 79 Male 28.0 186.0 21 183.0 5 Brown

e) Sample’s Test Statistic: 2.69 80 Female 23.0 161.0 26 161.5 4 Brown

f) P-value: 0.0071 81 Male 23.5 162.5 42 162.5 4 Blonde

CONCLUSION OF HYPOTHESIS TEST BASED ON TEST STATISTIC AND P-VALUE AND EXPLAIN WHY: 82 Female 27.0 169.0 31 170.0 1 Brown

as we can see that our p-value is 0.0071 which is less than level of significance(0.01) so we reject the null hypothsis 83 Female 23.5 165.0 28 165.0 1 Blonde

84 Male 28.0 180.0 25 172.0 5 Red

85 Female 25.5 176.0 21 172.0 9 Blonde

FINAL INTERPRETIVE SENTENCE: 86 Male 25.5 183.0 18 186.0 3 Brown

so therefore we conclude that not 58% of the students take elements of statistics online at FHSU come from families of size four or large. 87 Female 26.0 171.0 25 172.0 12 Brown

88 Female 24.0 175.5 38 176.0 6 Blonde

89 Female 22.0 165.0 27 167.0 11 Brown

90 Male 28.0 175.0 39 182.0 3 Black

91 Male 28.0 188.0 33 189.0 7 Brown

p 0.58 92 Female 24.0 167.5 18 163.5 5 Blonde

n 98 93 Female 20.5 167.5 36 153.5 5 Black

x 70 94 Female 22.0 171.0 19 174.0 4 Red

95 Male 26.0 180.5 28 180.5 5 Brown

96 Female 25.0 167.5 22 165.0 3 Brown

3. “It has been claimed that the mean foot length of adults in the U.S. is less than 26 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 based on the P-value is required in this problem.

After typing out a) and b) below, use scratch paper to identify all variables from the given information using the correct symbols (s, σ, µ, x-bar, n, p, α, etc.), then go to the templates tab in the Unit 3 Excel Guide (part 1) and determine which template to use, based on the claim in the problem. Copy and paste the entire template (including title) to the right of the problem using the instructions in the blue-shaded area above. Use cell references from the completed template to answer parts c) – g).

Next, give the conclusion of your hypothesis test (choose “”reject the null hypothesis”” or “”fail to reject the null hypothesis””) based on the test statistic and the p-value and explain why you chose your conclusion.

Finally, give an interpretive sentence. Follow examples given in the Unit 3 Excel Guide for correct wording.” 97 Female 25.5 154.0 23 155.5 7 Brown

98 Female 21.0 158.0 25 157.0 2 Brown

question 3

mean 24.8

st.dev 2.084731587

n 97

PROVIDE THE FOLLOWING INFORMATION. FOR EACH STATISTIC, USE A CELL REFERENCE FROM YOUR TEMPLATE:

a) H0: µ<26

b) H1: µ<26

c) Sample's Mean (x-bar): 24.8

d) Sample's S.D. (s): 2.08

e) Sample's Test Statistic: 2.58

f) P-value: 1

CONCLUSION OF HYPOTHESIS TEST BASED ON P-VALUE AND EXPLAIN WHY:

as our p value is 1 which is greater then 0.05 so we reject nul hypothesis

FINAL INTERPRETIVE SENTENCE:

so we can conclude that the average foot length of adul is greater than 26cm