MATH Assignment Chapter 23 complete solutions correct answers key

MATH Assignment Chapter 23 complete solutions correct answers key

Assignment Chapter 23.

Solutions and answers should be handwritten not typed. Make sure that you show you work when

appropriate.

1. A certain female middle-aged red-haired slightly confused professor wants to test a theory regarding Canadians’ favourite professional sport. Based on several national polls she thinks that Canadians would distributed according the following percentages:

Hockey 46%

Baseball 12%

Football 12%

Soccer 5%

Basketball 8%

No favourite professional sport 17%

She surveys her Math 2209 class and finds the following responses to question “Which is your favourite sport?”:

Hockey 10

Baseball 6

Football 4

Soccer 8

Basketball 3

No favourite professional sport 11

Use the Minitab output below to test if the professor is correct and significance level of 5%.

Test Contribution

Category Observed Proportion Expected to Chi-Sq

Hockey 10 0.46 ? ?

Baseball 6 0.12 5.04 0.18286

Football 4 0.12 5.04 0.21460

Basketball and Soccer 11 0.13 5.46 5.62117

No sport 11 0.17 7.14 2.08678

N DF Chi-Sq P-Value

42 ? 12.6014 ?

a) (2 pts) Determine if this is a test of goodness-of-fit, homogeneity or independence. Explain.

b) (2 pts) Explain why the professor reduced the number of categories from 6 to 5 categories.

c) (1 pt) Calculate the degrees of freedom. Show your calculation.

d) (2 pts) Calculate the expected value for the category Hockey.

e) (2 pts) Calculate the contribution to Chi-square for the category Hockey.

f) (1 pt). Show how the degrees of freedom are calculated.

g) (3 pts) State the test statistic from the Minitab output and look up the p-value using an appropriate table.

h) (2 pts) Briefly asses the significance and the strength of the evidence.

i) (4 pts) Draw a conclusion in context of the problem.

2. A UK study compared the acceptance of two proposed wind turbines sites north of Sheffield for five sampled communities. The two different sites are described below and their geographic locations are indicated with stars on the map.

Butterthwaite Farm is indicated with a B along the highway in the map below and Westwood Country

Park is indicated with a W (see arrows).

A random sample was obtained from each community, Thorpe Hesley [TH], Ecclesfield [EF], Chapeltown [CP], Shiregreen [SG] and High Green [HG]. A random sample was obtained from each community. For each proposed site individuals were asked to indicate if they accepted the proposed wind turbine development or not.

A Chi-square analysis was used to examine whether there was a difference between the five sampled communities with respect to the distribution in attitude to the development at each proposed wind turbine site.

Results for the proposed Butterwaite farm wind turbine site:

Yes_ No_ All

Thorpe Hesley 53 24 77

52.34 ?

0.00843 ?

Ecclesfield 57 27 84

57.09 26.91

0.00015 0.00033

Chapeltown 55 34 89

60.49 28.51

0.49864 1.05810

Shiregreen 42 18 60

40.78 19.22

0.03642 0.07729

High Green 54 20 74

50.30 23.70

0.27264 0.57854

All 261 123 384

Pearson Chi-Square = 2.548, DF = ?, P-Value = ?

Results for the proposed Westwood Country Park wind turbine site:

Yes No All

Thorpe Hesley 56 21 77

50.53 26.47

0.5919 1.1299

Ecclesfield 58 26 84

55.13 28.88

0.1499 0.2863

Chapeltown 59 30 89

58.41 30.59

0.0060 0.0115

Shiregreen 46 14 60

39.38 20.63

1.1147 2.1280

High Green 33 41 74

48.56 25.44

4.9872 9.5210

All 252 132 384

Pearson Chi-Square = 19.926, DF = ?, P-Value = ?

a) (2 pts) Determine if this is a test of goodness-of-fit, homogeneity or independence.

Explain.

b) (2 pts) For the proposed Butterwaite site, state the hypotheses for the chi-squared test, in plain English.

c) (1 pt) State the test statistic.

d) (1 pt) Determine the degrees of freedom are calculated (show your calculations).

e) (1 pt) Determine the p-value using the Chi-square table.

f) (2 pts) Show how the expected value is calculated for the top right cell, individuals in the

Thorpe Hesley community who are opposed to the wind turbine development at the proposed Butterwaite farm site.

g) (3 pts) Show how the contributions to the chi-square value is calculated for the top right cell, individuals in the Thorpe Hesley community who are opposed to the wind turbine development at the proposed Butterwaite farm site.

h) (1 pt) Give a brief assessment of the evidence.

i) (4 pts) Give a full conclusion in context.

j) (2 pts) For the Westwood Country Park site, state the hypotheses for the chi-squared test, in plain English.

k) (1 pt) State the test statistic.

l) (1 pt) Determine the degrees of freedom.

m) (1 pt) Find the p-value using the Chi-square table.

n) (1 pt) Give a brief assessment of the evidence.

o) (4 pts) Give a full conclusion in context.

p) Bonus question (3 pts). Compare the result of the Chi-squared tests for proposed wind turbine site Westwood Country Park and Butterwaite farm. Using the map and the information above, try to find a reason for the contrasting results for the two different proposed sites.