Math 102 Project 7

Project 7 Math 102

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Project 7 Round off answers to two decimal places. 50 Questions

1-19. Refer to the data below. Notice there are 50 people given with some being males and others being female. Next to each person is listed the

highest level of education that the person completed. Determine if

there is a significant relationship between the gender of the person and

his/her education level. Use α = 5%

Find the Observed values from the data, the expected values, Null

hypothesis, Alternate hypothesis, degrees of freedom, alpha, critical

chi square, computed chi square and decision (Reject Ho or Fail to

Reject Ho)

(Refer to the answer sheet – Answers 1-19)

Person # Gender Education Person # Gender Education 1 Male 4 year 26 Female HS

2 Male 4 year 27 Male HS

3 Female 4 year 28 Female HS

4 Female 4 year 29 Female HS

5 Female 4 year 30 Male HS

6 Male 4 year 31 Female HS

7 Female 4 year 32 Female HS

8 Male 4 year 33 Female HS

9 Female 4 year 34 Male HS

10 Female 4 year 35 Female HS

11 Female 2 year 36 Female HS

12 Male 2 year 37 Male HS

13 Female 2 year 38 Male HS

14 Male 2 year 39 Female HS

15 Female 2 year 40 Female HS

16 Male 2 year 41 Female HS

17 Female 2 year 42 Male HS

18 Male 2 year 43 Female HS

19 Female 2 year 44 Female HS

20 Male 2 year 45 Female HS

21 Female 2 year 46 Male HS

22 Female 2 year 47 Male HS

23 Female 2 year 48 Female HS

24 Female 2 year 49 Male HS 25 Female 2 year 50 Female HS

Project 7 Math 102

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20 - 26 . In an experiment designed to compare the effectiveness of different brands of pain relievers, a group of 320 individuals who

complained of chronic pain were randomly assigned to three daily

treatments: three tablets of Brand A, three tablets of Brand B or

three placebos. After taking the treatments, each subject was questioned, to

determine the effectiveness of their treatment. Their responses are

classified in the table below. Based upon these sample results can one conclude that drug

treatment and relief from pain are independent at a significance

level of 1%.

Find the expected values, Null hypothesis, Alternate hypothesis,

degrees of freedom, alpha, critical chi square, computed chi square

and decision (Reject Ho or Fail to Reject Ho)

Even though you have to calculate Expected values

you do not show them for this example 2, on the

answer sheet.

(Refer to answer sheet – Answers 20 -26)

27-32 Matthew, a medical researcher, wants to determine if a positive linear

relationship exists between the numbers of pounds a male is overweight and his

blood pressure. He randomly selects a sample of 10 males and records the

number of pounds that the individuals are over his “ideal” weight according to a

medical weight chart and his systolic blood pressure. Mathew’s sample data is

listed in the table below.

27 Find the correlation between number of pounds over ideal weight and blood

pressure.

28 Find the value of a in the formula y = a+bx

29 Find the value of b in the formula y = a+bx

30 Make a prediction for blood pressure(y) for the weight(x) given on the answer

sheet.

31 Find the value of coefficient of determination

32

What percent of the variance in the blood pressure is accounted for by the

variance in pounds over ideal weight?

RESULTS BRAND A BRAND B PLACEBO TOTALS

Total Relief 25 31 20 76

Some Relief 27 36 31 94

No Relief 47 58 45 150

Totals 99 125 96 320

Project 7 Math 102

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Data Male Subject Pounds Overweight(x) Blood Pressure(y)

1 12 150

2 8 142

3 20 165

4 17 152

5 14 147

6 23 158

7 6 135

8 4 128

9 15 135

10 19 153

33 - 38

Craig, a marketing executive for a brewery company, wants to determine if

there is a positive linear relationship between advertising expenditures and

sales for their new lite beer product, Less Ale. He randomly samples 7 sales

regions and records the sample data in the following table, where the x

variable represents the advertising expenditure in thousands of dollars and the

y variable represents the beer sales in million dollars.

33 Find the correlation between advertising expenditures (x) and sales(y).

34 Find the value of a in the formula y = a+bx

35 Find the value of b in the formula y = a+bx

36 Make a prediction for sales(y) for the advertising expenditures(x) given on the

answer sheet.

37 Find the value of coefficient of determination

38 What percent of the variance in the sales is accounted for by the variance in

advertising expenditures?

Data Region # Expenditure(x) Sales(y)

1 32 38

2 43 35

3 63 42

4 92 50

5 57 40

6 23 35

7 84 41

Project 7 Math 102

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39 - 44

I.M.Smart, a statistics nerd, wants to investigate if there is a positive

relationship between the number of hours a student studies for a statistics exam

and the student’s test grade. He randomly samples 12 students that are taking

statistics at a community college and records the sample data in the following

data.

39 Find the correlation between advertising expenditures (x) and sales(y).

40 Find the value of a in the formula y = a+bx

41 Find the value of b in the formula y = a+bx

42 Make a prediction for Test Grade(y) for the Studying Hours(x) given on the

answer sheet.

43 Find the value of coefficient of determination

44 What percent of the variance in the Test Grades is accounted for by the

variance in Studying Hours?

Student # Studying Hours Test Grade

1 10 80

2 8 60

3 12 78

4 20 90

5 7 65

6 4 60

7 9 70

8 15 85

9 11 75

10 6 70

11 2 45

12 1 50

Project 7 Math 102

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45-50 Unrelated questions.

45

Does the scatter diagram display a relationship between the two variables and

if so, is it positive or negative

a) positive b) negative c) none

46 Does the scatter diagram display a relationship between the two variables and

if so, is it positive or negative

a) positive b) negative c) none

47 If a scattergram displays data points that approach a line that rises as your

eyes move left to right, the correlation will be closer to which value?

a) +1 b) -1 c) 0 d) can not determine 48 Which of the following correlations represents the least amount of

relationship between two variables?

a) -1 b) -.78 c) 0.15 d) 0.0 49 In Chi Square, if the conclusion is that the classifications are independent then

the Calculated Pearson’s chi- square test statistics is greater the Table critical

chi square.

a) True b) Sometimes true c) False d) Can not determine 50 The shape of the chi square distribution is similar to the shape of the

t-distribution.

a) True b) Sometimes true c) False d) Can not determine