STA6507 – Nonparametric Statistics

Fall 2021

Due at 11:59 pm on November 18, 2020

In this assignment we will practice using tests for contingency tables and rank-based tests; submit your code R with your solutions (R Markdown is preferred). Solve all problems but only two will be graded. Put those that you want me to grade at the beginning of your solution.

Problem 1

One hundred men and 100 women were asked to try a new toothpaste and to state whether they liked or did not like the new taste. 32 men and 26 women said they did not like the new taste. Does this indicate a difference in preferences between men and women in general?

Problem 2

A quick test for correlation between two variables X and Y, each of which has at least an ordinal scale of measurement, can be performed using the Fishers exact test. The procedure is as follows:

Divide the scatter plot of the N values of (X,Y) with a vertical line at the median of X.

Divide the scatter plot of the N values of (X,Y) with a horizontal line at the median of Y. Count the number of observations in each of the four quadrants. Note that the row and

column totals are N/2, and are not random.

Suppose that 16 observations pairs of X = age of marriage of a husband, and Y=age of marriage of his father, resulted on 7 pairs where both ages were above the median. Are the two variables positively correlated?

Problem 3

A random sample of stocks from the American Stock Exchange (ASE) is compared with a random sample of stocks from the New York Stock Exchange to see if any difference in the rating percent-ages of the two exchanges. Of the 23 stocks from the ASE there were 11 As, 11 Bs, and 1 C. Of the 35 stocks from the NYSE there were 24 As, 11 Bs, and no Cs.

What does your analysis look like?

1

Problem 4

A television-marketing rm would like to determine if the time of the ad appeared in television is related to the product being sold. The number of responses to the products rm is as follows:

Product

Fishing Rod

Kitchen Tool

Music CD

Exercise Machine

Daytime

6

73

55

7

Nighttime

14

65

82

8

Weekend

21

58

48

8

What does your analysis look like?

Calculate and comment the Cramer’s Contingency Coefficient.

Problem 5

Test the hypothesis that the following samples were obtained from populations having the same medians.

Sample1: 35, 42, 42, 30, 15, 31, 29, 29, 17

Sample2: 34, 38, 26, 17, 42, 28, 35, 33, 16

Sample3: 17, 29, 30, 36, 41, 30, 31, 23, 38

Problem 6

Random samples from each of three different types of light bulbs were tested to see how long the light bulbs lasted, with the following results:

A

73

64

67

62

B

84

80

81

77

C

82

79

71

75

Do these results indicate a significant difference between brands?

Problem 7

A blood bank kept a record of the rate of heartbeats for several blood donors.

Men

58

65

74

74

76

79

82

86

Women

66

68

67

69

72

73

74

75

76

1. Is the average of the rate of heartbeats the same for men and women?

2

Problem 8

7 married couples were selected at random, and each husband and each wife were asked how much money they spent on their spouses Christmas present year. The responses were as follows:

Couple

1

2

3

4

5

6

7

Husband

25

21

38

64

52

16

26

Wife

16

42

56

41

19

26

24

1. Does the husband tend to spend more than the wife?

3[supanova_question]

## Assignment 4 STA6507 – Nonparametric Statistics Fall 2021 Due at 11:59 pm

Assignment 4

STA6507 – Nonparametric Statistics

Fall 2021

Due at 11:59 pm on November 18, 2020

In this assignment we will practice using tests for contingency tables and rank-based tests; submit your code R with your solutions (R Markdown is preferred). Solve all problems but only two will be graded. Put those that you want me to grade at the beginning of your solution.

Problem 1

One hundred men and 100 women were asked to try a new toothpaste and to state whether they liked or did not like the new taste. 32 men and 26 women said they did not like the new taste. Does this indicate a difference in preferences between men and women in general?

Problem 2

A quick test for correlation between two variables X and Y, each of which has at least an ordinal scale of measurement, can be performed using the Fishers exact test. The procedure is as follows:

Divide the scatter plot of the N values of (X,Y) with a vertical line at the median of X.

Divide the scatter plot of the N values of (X,Y) with a horizontal line at the median of Y. Count the number of observations in each of the four quadrants. Note that the row and

column totals are N/2, and are not random.

Suppose that 16 observations pairs of X = age of marriage of a husband, and Y=age of marriage of his father, resulted on 7 pairs where both ages were above the median. Are the two variables positively correlated?

Problem 3

A random sample of stocks from the American Stock Exchange (ASE) is compared with a random sample of stocks from the New York Stock Exchange to see if any difference in the rating percent-ages of the two exchanges. Of the 23 stocks from the ASE there were 11 As, 11 Bs, and 1 C. Of the 35 stocks from the NYSE there were 24 As, 11 Bs, and no Cs.

What does your analysis look like?

1

Problem 4

A television-marketing rm would like to determine if the time of the ad appeared in television is related to the product being sold. The number of responses to the products rm is as follows:

Product

Fishing Rod

Kitchen Tool

Music CD

Exercise Machine

Daytime

6

73

55

7

Nighttime

14

65

82

8

Weekend

21

58

48

8

What does your analysis look like?

Calculate and comment the Cramer’s Contingency Coefficient.

Problem 5

Test the hypothesis that the following samples were obtained from populations having the same medians.

Sample1: 35, 42, 42, 30, 15, 31, 29, 29, 17

Sample2: 34, 38, 26, 17, 42, 28, 35, 33, 16

Sample3: 17, 29, 30, 36, 41, 30, 31, 23, 38

Problem 6

Random samples from each of three different types of light bulbs were tested to see how long the light bulbs lasted, with the following results:

A

73

64

67

62

B

84

80

81

77

C

82

79

71

75

Do these results indicate a significant difference between brands?

Problem 7

A blood bank kept a record of the rate of heartbeats for several blood donors.

Men

58

65

74

74

76

79

82

86

Women

66

68

67

69

72

73

74

75

76

1. Is the average of the rate of heartbeats the same for men and women?

2

Problem 8

7 married couples were selected at random, and each husband and each wife were asked how much money they spent on their spouses Christmas present year. The responses were as follows:

Couple

1

2

3

4

5

6

7

Husband

25

21

38

64

52

16

26

Wife

16

42

56

41

19

26

24

1. Does the husband tend to spend more than the wife?

3[supanova_question]

## Assignment 4 STA6507 – Nonparametric Statistics Fall 2021 Due at 11:59 pm

Assignment 4

STA6507 – Nonparametric Statistics

Fall 2021

Due at 11:59 pm on November 18, 2020

In this assignment we will practice using tests for contingency tables and rank-based tests; submit your code R with your solutions (R Markdown is preferred). Solve all problems but only two will be graded. Put those that you want me to grade at the beginning of your solution.

Problem 1

One hundred men and 100 women were asked to try a new toothpaste and to state whether they liked or did not like the new taste. 32 men and 26 women said they did not like the new taste. Does this indicate a difference in preferences between men and women in general?

Problem 2

A quick test for correlation between two variables X and Y, each of which has at least an ordinal scale of measurement, can be performed using the Fishers exact test. The procedure is as follows:

Divide the scatter plot of the N values of (X,Y) with a vertical line at the median of X.

Divide the scatter plot of the N values of (X,Y) with a horizontal line at the median of Y. Count the number of observations in each of the four quadrants. Note that the row and

column totals are N/2, and are not random.

Suppose that 16 observations pairs of X = age of marriage of a husband, and Y=age of marriage of his father, resulted on 7 pairs where both ages were above the median. Are the two variables positively correlated?

Problem 3

A random sample of stocks from the American Stock Exchange (ASE) is compared with a random sample of stocks from the New York Stock Exchange to see if any difference in the rating percent-ages of the two exchanges. Of the 23 stocks from the ASE there were 11 As, 11 Bs, and 1 C. Of the 35 stocks from the NYSE there were 24 As, 11 Bs, and no Cs.

What does your analysis look like?

1

Problem 4

A television-marketing rm would like to determine if the time of the ad appeared in television is related to the product being sold. The number of responses to the products rm is as follows:

Product

Fishing Rod

Kitchen Tool

Music CD

Exercise Machine

Daytime

6

73

55

7

Nighttime

14

65

82

8

Weekend

21

58

48

8

What does your analysis look like?

Calculate and comment the Cramer’s Contingency Coefficient.

Problem 5

Test the hypothesis that the following samples were obtained from populations having the same medians.

Sample1: 35, 42, 42, 30, 15, 31, 29, 29, 17

Sample2: 34, 38, 26, 17, 42, 28, 35, 33, 16

Sample3: 17, 29, 30, 36, 41, 30, 31, 23, 38

Problem 6

Random samples from each of three different types of light bulbs were tested to see how long the light bulbs lasted, with the following results:

A

73

64

67

62

B

84

80

81

77

C

82

79

71

75

Do these results indicate a significant difference between brands?

Problem 7

A blood bank kept a record of the rate of heartbeats for several blood donors.

Men

58

65

74

74

76

79

82

86

Women

66

68

67

69

72

73

74

75

76

1. Is the average of the rate of heartbeats the same for men and women?

2

Problem 8

7 married couples were selected at random, and each husband and each wife were asked how much money they spent on their spouses Christmas present year. The responses were as follows:

Couple

1

2

3

4

5

6

7

Husband

25

21

38

64

52

16

26

Wife

16

42

56

41

19

26

24

1. Does the husband tend to spend more than the wife?

3[supanova_question]

## Assignment 4 STA6507 – Nonparametric Statistics Fall 2021 Due at 11:59 pm

Writing Assignment Help Assignment 4

STA6507 – Nonparametric Statistics

Fall 2021

Due at 11:59 pm on November 18, 2020

Problem 1

Problem 2

Divide the scatter plot of the N values of (X,Y) with a vertical line at the median of X.

column totals are N/2, and are not random.

Problem 3

What does your analysis look like?

1

Problem 4

Product

Fishing Rod

Kitchen Tool

Music CD

Exercise Machine

Daytime

6

73

55

7

Nighttime

14

65

82

8

Weekend

21

58

48

8

What does your analysis look like?

Calculate and comment the Cramer’s Contingency Coefficient.

Problem 5

Sample1: 35, 42, 42, 30, 15, 31, 29, 29, 17

Sample2: 34, 38, 26, 17, 42, 28, 35, 33, 16

Sample3: 17, 29, 30, 36, 41, 30, 31, 23, 38

Problem 6

A

73

64

67

62

B

84

80

81

77

C

82

79

71

75

Do these results indicate a significant difference between brands?

Problem 7

A blood bank kept a record of the rate of heartbeats for several blood donors.

Men

58

65

74

74

76

79

82

86

Women

66

68

67

69

72

73

74

75

76

1. Is the average of the rate of heartbeats the same for men and women?

2

Problem 8

Couple

1

2

3

4

5

6

7

Husband

25

21

38

64

52

16

26

Wife

16

42

56

41

19

26

24

1. Does the husband tend to spend more than the wife?

## Assignment 4 STA6507 – Nonparametric Statistics Fall 2021 Due at 11:59 pm

Assignment 4

STA6507 – Nonparametric Statistics

Fall 2021

Due at 11:59 pm on November 18, 2020

Problem 1

Problem 2

Divide the scatter plot of the N values of (X,Y) with a vertical line at the median of X.

column totals are N/2, and are not random.

Problem 3

What does your analysis look like?

1

Problem 4

Product

Fishing Rod

Kitchen Tool

Music CD

Exercise Machine

Daytime

6

73

55

7

Nighttime

14

65

82

8

Weekend

21

58

48

8

What does your analysis look like?

Calculate and comment the Cramer’s Contingency Coefficient.

Problem 5

Sample1: 35, 42, 42, 30, 15, 31, 29, 29, 17

Sample2: 34, 38, 26, 17, 42, 28, 35, 33, 16

Sample3: 17, 29, 30, 36, 41, 30, 31, 23, 38

Problem 6

A

73

64

67

62

B

84

80

81

77

C

82

79

71

75

Do these results indicate a significant difference between brands?

Problem 7

A blood bank kept a record of the rate of heartbeats for several blood donors.

Men

58

65

74

74

76

79

82

86

Women

66

68

67

69

72

73

74

75

76

1. Is the average of the rate of heartbeats the same for men and women?

2

Problem 8

Couple

1

2

3

4

5

6

7

Husband

25

21

38

64

52

16

26

Wife

16

42

56

41

19

26

24

1. Does the husband tend to spend more than the wife?

3[supanova_question]

## Assignment 4 STA6507 – Nonparametric Statistics Fall 2021 Due at 11:59 pm

Assignment 4

STA6507 – Nonparametric Statistics

Fall 2021

Due at 11:59 pm on November 18, 2020

Problem 1

Problem 2

Divide the scatter plot of the N values of (X,Y) with a vertical line at the median of X.

column totals are N/2, and are not random.

Problem 3

What does your analysis look like?

1

Problem 4

Product

Fishing Rod

Kitchen Tool

Music CD

Exercise Machine

Daytime

6

73

55

7

Nighttime

14

65

82

8

Weekend

21

58

48

8

What does your analysis look like?

Calculate and comment the Cramer’s Contingency Coefficient.

Problem 5

Sample1: 35, 42, 42, 30, 15, 31, 29, 29, 17

Sample2: 34, 38, 26, 17, 42, 28, 35, 33, 16

Sample3: 17, 29, 30, 36, 41, 30, 31, 23, 38

Problem 6

A

73

64

67

62

B

84

80

81

77

C

82

79

71

75

Do these results indicate a significant difference between brands?

Problem 7

A blood bank kept a record of the rate of heartbeats for several blood donors.

Men

58

65

74

74

76

79

82

86

Women

66

68

67

69

72

73

74

75

76

1. Is the average of the rate of heartbeats the same for men and women?

2

Problem 8

Couple

1

2

3

4

5

6

7

Husband

25

21

38

64

52

16

26

Wife

16

42

56

41

19

26

24

1. Does the husband tend to spend more than the wife?

3[supanova_question]