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```					STA 213, Fall 2011, StatCrunch Assignment #5 - Solution

Exercise 13.90
π1: true proportion of all customers that purchased the warranty when the product was sold at the regular price
π2: true proportion of all customers that purchased the warranty when the product was sold at the sale price
Test Statistic: Z  ( p1  p2 )  0 ;
H0 : p1 - p2 = 0;    HA : p1 - p2 > 0;
ˆ    ˆ                 Accept HA if P-value <         = .10
( p p
ˆ
1  ˆ2)

Calculations: Hypothesis test results:
Difference Count1 Total1 Count2 Total2 Sample Diff. Std. Err.                       Z-Stat     P-value

p1 - p2              47    229         25       178    0.06479073      0.03813      1.6992        0.0446

[So, accept HA ]
Interpretation: At the 10% significance level there is sufficient evidence to say the true proportion of all customers purchasing the warranty is
higher when the product is sold at the regular price than at the sale price.

Exercise 13.92
p1: true proportion of all people with credit score below 600 that default on their loan
p2: true proportion of all people with credit score 600 and above that default on their loan.
Test Statistic: Z  ( p1  p2 )  0 ;
H0 : p1 - p2 = 0;    HA : p1 - p2 > 0;
ˆ    ˆ                 Accept HA if P-value <         = .10
( p p
ˆ
1  ˆ2)

Calculations: Hypothesis test results:
Difference Count1 Total1 Count2 Total2 Sample Diff. Std. Err. Z-Stat P-value

p1 - p2              11    562             7    804         0.0109     0.00627      1.733     0.0415

[So, accept HA ]
Interpretation: At the 10% significance level there is sufficient evidence to say the true proportion of borrowers with credit score below 600 that
default on their loan is greater than the true proportion of all borrowers with credit score 600 and above that default on their loan. Yes, people
with lower credit score are more likely to default.

Exercise 13.101
p1: true proportion of all Lexus owners that plan to buy another Lexus for their next car.
p2: true proportion of all Acura owners that plan to buy another Acura for their next car.
Test Statistic: Z  ( p1  p2 )  0 ;
H0 : p1 - p2 = 0;   HA : p1 - p2 ≠ 0;
ˆ    ˆ                 Accept HA if P-value <         = .05
( p p
ˆ
1  ˆ2)

Calculations: Hypothesis test results:
Difference     Count1 Total1 Count2 Total2              Sample Diff.    Std. Err.     Z-Stat       P-value

p1 - p2              317    350        261        294        0.01796       0.02399     0.7485       0.4541

[So, do not accept HA ]
Interpretation: At the 5% significance level there is not sufficient evidence to say the true proportion of all Lexus owners that would buy another
Lexus is any different from the true proportion of all Acura owners that would buy another Acura. Thus, we cannot say they have different
satisfaction levels.
Exercise 13.102
a. p1: true proportion of all smokers that suffer from some form of heart disease;
p2: true proportion of all non-smokers that suffer from some form of heart disease;
Test Statistic: Z  ( p1  p2 )  0 ;
H0 : p1 - p2 = 0;        HA : p1 - p2 > 0;
ˆ    ˆ                        Accept HA if P-value <      = .10
( p p
ˆ  ˆ
1   2)

Hypothesis test results:
Difference Count1 Total1 Count2 Total2 Sample Diff.                           Std. Err.       Z-Stat       P-value

p1 - p2             10         38         12         162        0.18908381       0.056397     3.35273        0.0004

[So, accept HA ]
Interpretation: At the 10% significance level there is sufficient evidence to say the true proportion of all smokers that suffer some form of heart
disease is greater than the true proportion of non-smokers that suffer some form of heart disease.

b.   p1: true proportion of all smokers that suffer from some form of heart disease;
p2: true proportion of all non-smokers that suffer from some form of heart disease;
Formula:   ( p1  p2 )  Z   ( p1  p2 )
ˆ ˆ                 ˆ ˆ

90% confidence interval results:
Difference Count1 Total1 Count2 Total2 Sample Diff.                           Std. Err.      L. Limit        U. Limit

p1 - p2             10         38         12         162     0.18908381        0.074338       0.066808        0.31136

Interpretation: We estimate with 90% confidence the true proportion of all smokers that suffer some form of heart disease is between 6.68% and
31.4% greater than the true proportion of all non-smokers that suffer some form of heart disease.

Exercise 13.106
p1: true proportion of all workers with just a high school education that work 11 or more hours per day
p2: true proportion of all workers with a post secondary education that work 11 or more hours per day
Test Statistic: Z  ( p1  p2 )  0 ;
H0 : p1 - p2 = 0;        HA : p1 - p2 > 0;
ˆ    ˆ                        Accept HA if P-value <      = .05
( p p
ˆ  ˆ
1   2)

Calculations: Hypothesis test results:
Difference Count1 Total1 Count2 Total2 Sample Diff. Std. Err.                            Z-Stat        P-value

p1 - p2              167        194         63          80       0.07332474 0.048783 1.5030777         0.0664

[So, do not accept HA ]
Interpretation: At the 5% significance level there is not sufficient evidence to say the true proportion of all workers with just a high school
education that work 11 or more hours per day is any greater than the proportion of all workers with a post secondary education that work 11 or
more hours per day. We cannot infer that those with more education are less likely to work 11 or more hours per day.
Exercise 13.126
a. p1: true proportion of all boys in 2001 that participated in organized sports
p2: true proportion of all boys in 2011 that participated in organized sports
Test Statistic: Z  ( p1  p2 )  0 ;
H0 : p1 - p2 = 0;        HA : p1 - p2 > 0;
ˆ    ˆ                  Accept HA if P-value <        = .05
( p p
ˆ  ˆ
1   2)

Calculations: Hypothesis test results:
Difference Count1 Total1 Count2 Total2                      Sample Diff.   Std. Err.     Z-Stat        P-value

p1 - p2                  178    271      174      313        0.10091603     0.04060 2.4854672           0.0065

[So, do accept HA ]
Interpretation: At the 5% significance level there is sufficient evidence to say the true proportion of all boys in 2001 that participated in
organized sports is greater than the true proportion of all boys in 2011 that participated in organized sports. We can infer that sports
participation has decreased for boys in the last decade.

b.   p1: true proportion of all girls in 2001 that participated in organized sports
p2: true proportion of all girls in 2011 that participated in organized sports
Test Statistic: Z  ( p1  p2 )  0 ;
H0 : p1 - p2 = 0;        HA : p1 - p2 > 0;
ˆ    ˆ                  Accept HA if P-value <        = .05
( p p
ˆ  ˆ
1   2)

Calculations: Hypothesis test results:
Difference Count1 Total1 Count2 Total2                      Sample Diff.   Std. Err.     Z-Stat        P-value

p1 - p2                  137    281      137      304       0.036886588     0.04129 0.8932662           0.1859

[So, do not accept HA ]
Interpretation: At the 5% significance level there is not sufficient evidence to say the true proportion of all girls in 2001 that participated in
organized sports is greater than the true proportion of all girls in 2011 that participated in organized sports. We cannot infer that sports
participation has decreased for girls in the last decade.

c.   p1: true proportion of all boys in 2011 that participated in organized sports
p2: true proportion of all girls in 2011 that participated in organized sports
Test Statistic: Z  ( p1  p2 )  0 ;
H0 : p1 - p2 = 0;        HA : p1 - p2 > 0;
ˆ    ˆ                  Accept HA if P-value <        = .05
( p p
ˆ  ˆ
1   2)

Calculations: Hypothesis test results:
Difference Count1 Total1 Count2 Total2                      Sample Diff.   Std. Err.     Z-Stat        P-value

p1 - p2                  174    313      137      304       0.105252646 0.040261 2.6142292              0.0045

[So, do accept HA ]
Interpretation: At the 5% significance level there is sufficient evidence to say the true proportion of all boys in 2011 that participated in
organized sports is greater than the true proportion of all girls in 2011 that participated in organized sports. Yes, we can infer that girls are less
likely to participate in organized sports this year.

Exercise 13.132
p1: true proportion of all drivers that wear their seat belts last year
p2: true proportion of all drivers that wear their seat belts this year
Test Statistic: Z  ( p1  p2 )  0 ;
H0 : p1 - p2 = 0;        HA : p1 - p2 > 0;
ˆ    ˆ                Accept HA if P-value <        = .10
( p p
ˆ  ˆ1    2)

Hypothesis test results:
Difference Count1 Total1 Count2 Total2 Sample Diff. Std. Err.                          Z-Stat         P-value

p1 - p2                  221   327      288     382     -0.07808572        0.03390     -2.30317        0.0106

[So, accept HA ]
Interpretation: At the 5% significance level there is sufficient evidence to say the true proportion of all drivers that wear their seat belts last year
is less than the true proportion of all drivers that wear their seat belts this year. Thus, yes there is evidence of significantly higher seat belt usage.

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