Name: ___________________________

Intermediate Statistics Spring 2010 Final Exam

Directions: For the multiple choice items, choose the best answer and place your response on the line to the left of the problem. For the short answer items, be sure to show ALL of your work in order to receive partial credit.

______ 1. A random sample of n = 4 scores is obtained from a normal population with μ = 20 and σ = 4. What is the probability of obtaining a mean greater than X = 22 for this sample?

A.

.1587

B.

.3085

C.

.1922

D.

.5

______ 2. The null hypothesis:

A.

states that the treatment has no effect.

B.

is always stated in terms of sample statistics.

C.

is denoted by the symbol H1.

D.

All of the choices are correct.

______ 3. If the researcher sets the alpha level at .01 for a two-tailed test, which of the following represents the critical regions for that alpha level?

A.

z < -1; z > 1

B.

z < -2.30; z > 2.30

C.

z < -2.58; z > 2.58

D.

z < -1.96; z > 1.96

______ 4. If the standardized z-score of an individual’s score on an IQ test is -2.48, how many standard deviations away from the mean IQ score does this person’s score lie?

A.

More than 2 standard deviations above

B.

Less than 2 standard deviations below

C.

More than 2 standard deviations below

D.

Less than 2 standard deviations above

______ 5. After 5 points are subtracted from every score in a distribution, the mean is calculated and found to be μ = 65. What was the value of the mean for the original distribution?

A.

60

B.

65

C.

70

D.

Not enough information provided

Questions 6-9 refer to the following information:

A toy company is designing a type of educational toy cube for children and they want to find out what color children like best. To find out this information, they administered a survey and asked children about their color preference for this product. A child was instructed to circle the number in front of the color to indicate that s/he liked that color and each child is allowed to circle only one color.

1.

Red 5. Silver

2.

Yellow 6. Black

3.

Blue 7. Purple

4.

Green 8. Others

The results of the survey were as follows:

Color

Freq

1

20

2

30

3

25

4

13

5

20

6

29

7

16

8

43

6. Is the scale of measurement nominal, ordinal, interval, or ratio?

7. What is the mode of the data?

______ 8. Which of the following would best describe the central tendency of the distribution?

A.

mean

B.

median

C.

mode

9. Is it reasonable to use variance to describe the variability of this group of data? Briefly state your reason (less than 10 words)

Use the following scenario for Questions 10–13.

An educator wants to determine whether early exposure to school will affect IQ. He enlists the aid of the parents of 12 pairs of preschool-age identical twins who agree to let their twins participate in this experiment. One member of each twin pair is enrolled in preschool for 2 years while the other member of each pair remains at home. At the end of the 2 years, the IQs of all the children are measured. Assume the distribution of IQs is normal. The following information is provided:

α = .05 s2 = 9.9 DX = -2

IQs of students in Preschool

IQs of students at Home

1

110

114

2

121

118

3

107

103

4

117

112

5

115

117

6

112

106

7

130

125

8

116

113

9

111

109

10

120

122

11

117

116

12

106

104

______ 10. Assume that the formula is (home – preschool). If this is the case, which group had higher IQ scores?

A.

home

B.

preschool

C.

They had the same IQ scores.

______ 11. The two lowest scores were accidentally deleted from the Preschool sample. How does this deletion affect the mean of the Preschool sample?

A.

The mean has been increased.

B.

The mean has been decreased.

C.

The mean has remained the same.

D.

Not enough information available

______ 12. Which test should be used to conduct a hypothesis test on this data?

A.

Chi-square test

B.

one sample t test

C.

independent measures t test

D.

dependent measures t test

13. Conduct a hypothesis test to determine whether there is a significant difference in preschool and home IQs. Include all steps, and clearly state your conclusion as it specifically relates to this problem. (Note: “I reject/retain the null hypothesis is not sufficient.”)

14. A student is given a 5 option (A, B, C, D) multiple choice exam. For any given item, what would be the probability of the student answering the item correctly, assuming each option has an equally likely chance of being selected?

15. Suppose the entire test is comprised of 40 items. What would be the probability of answering at least 36 items correctly if p = .20?

16. A college is concerned that recent cohorts of students have less motivation to succeed than earlier cohorts of students. To assess their concern, they gave a standardized measure of achievement orientation to a random sample of college freshmen in 2009. They compared their achievement orientation scores (which ranged from 0 – 100) to norms of U.S. college freshmen from 2004 who had μ = 85 and σ = 4.

a.

What type of analysis (type of hypothesis test) would you perform to test whether current college freshmen differ from college freshmen in 2004? Justify your answer.

b.

Identify the dependent variable.

c.

What is the scale of measurement for the dependent variable? (nominal, ordinal, interval, or ratio)

17. Given the following numbers below, which measure of central tendency would be more appropriate—mean or median? Justify your answer.

22 37 14 17 27 41 30 13

19 21 29 37 29 20 16 17

34 16 35 80 16 12 24 29

18. For a population with μ = 100 and σ = 20, what is the X value corresponding to z = -0.55?

19. If μ = 400 and σ = 100, what is the probability of selecting at random a score less than or equal to 470?

20. A research wanted to see whether there was a relationship between smoking and residing area so he conducted a survey of 200 people. The results are shown in the following table.

Smoking Habit

Yes

No

Rural

45

55

City

35

65

a.

Fill in the table for the expected counts.

Smoking Habit

Yes

No

Rural

City

b.

Calculate the value of the chi-square statistic.

c.

What are the degrees of freedom?

d.

Do you reject or retain the null hypothesis for α=.05?

e.

What would you conclude? (Note: “I reject/retain the null hypothesis is not sufficient.”)

21. With the growth of cell phone providers, a researcher decides to examine whether there is a correlation between cost of cell phone service per month (rounded to the nearest dollar) and degree of customer satisfaction (on a scale of 1 - 10 with a 1 being not at all satisfied and a 10 being extremely satisfied). The researcher only includes programs with comparable types of services. A sample of the data is provided below.

dollars

satisfaction

41

6

48

8

47

10

45

4

39

9

35

6

42

3

49

5

52

2

55

10

a. What is the Pearson correlation coefficient?

b. Based on the correlation, would you say there is a relationship between cell phone provider price and level of satisfaction? Justify your answer.

Enjoy Your Summer!

Intermediate Statistics Spring 2010 Final Exam

Directions: For the multiple choice items, choose the best answer and place your response on the line to the left of the problem. For the short answer items, be sure to show ALL of your work in order to receive partial credit.

______ 1. A random sample of n = 4 scores is obtained from a normal population with μ = 20 and σ = 4. What is the probability of obtaining a mean greater than X = 22 for this sample?

A.

.1587

B.

.3085

C.

.1922

D.

.5

______ 2. The null hypothesis:

A.

states that the treatment has no effect.

B.

is always stated in terms of sample statistics.

C.

is denoted by the symbol H1.

D.

All of the choices are correct.

______ 3. If the researcher sets the alpha level at .01 for a two-tailed test, which of the following represents the critical regions for that alpha level?

A.

z < -1; z > 1

B.

z < -2.30; z > 2.30

C.

z < -2.58; z > 2.58

D.

z < -1.96; z > 1.96

______ 4. If the standardized z-score of an individual’s score on an IQ test is -2.48, how many standard deviations away from the mean IQ score does this person’s score lie?

A.

More than 2 standard deviations above

B.

Less than 2 standard deviations below

C.

More than 2 standard deviations below

D.

Less than 2 standard deviations above

______ 5. After 5 points are subtracted from every score in a distribution, the mean is calculated and found to be μ = 65. What was the value of the mean for the original distribution?

A.

60

B.

65

C.

70

D.

Not enough information provided

Questions 6-9 refer to the following information:

A toy company is designing a type of educational toy cube for children and they want to find out what color children like best. To find out this information, they administered a survey and asked children about their color preference for this product. A child was instructed to circle the number in front of the color to indicate that s/he liked that color and each child is allowed to circle only one color.

1.

Red 5. Silver

2.

Yellow 6. Black

3.

Blue 7. Purple

4.

Green 8. Others

The results of the survey were as follows:

Color

Freq

1

20

2

30

3

25

4

13

5

20

6

29

7

16

8

43

6. Is the scale of measurement nominal, ordinal, interval, or ratio?

7. What is the mode of the data?

______ 8. Which of the following would best describe the central tendency of the distribution?

A.

mean

B.

median

C.

mode

9. Is it reasonable to use variance to describe the variability of this group of data? Briefly state your reason (less than 10 words)

Use the following scenario for Questions 10–13.

An educator wants to determine whether early exposure to school will affect IQ. He enlists the aid of the parents of 12 pairs of preschool-age identical twins who agree to let their twins participate in this experiment. One member of each twin pair is enrolled in preschool for 2 years while the other member of each pair remains at home. At the end of the 2 years, the IQs of all the children are measured. Assume the distribution of IQs is normal. The following information is provided:

α = .05 s2 = 9.9 DX = -2

IQs of students in Preschool

IQs of students at Home

1

110

114

2

121

118

3

107

103

4

117

112

5

115

117

6

112

106

7

130

125

8

116

113

9

111

109

10

120

122

11

117

116

12

106

104

______ 10. Assume that the formula is (home – preschool). If this is the case, which group had higher IQ scores?

A.

home

B.

preschool

C.

They had the same IQ scores.

______ 11. The two lowest scores were accidentally deleted from the Preschool sample. How does this deletion affect the mean of the Preschool sample?

A.

The mean has been increased.

B.

The mean has been decreased.

C.

The mean has remained the same.

D.

Not enough information available

______ 12. Which test should be used to conduct a hypothesis test on this data?

A.

Chi-square test

B.

one sample t test

C.

independent measures t test

D.

dependent measures t test

13. Conduct a hypothesis test to determine whether there is a significant difference in preschool and home IQs. Include all steps, and clearly state your conclusion as it specifically relates to this problem. (Note: “I reject/retain the null hypothesis is not sufficient.”)

14. A student is given a 5 option (A, B, C, D) multiple choice exam. For any given item, what would be the probability of the student answering the item correctly, assuming each option has an equally likely chance of being selected?

15. Suppose the entire test is comprised of 40 items. What would be the probability of answering at least 36 items correctly if p = .20?

16. A college is concerned that recent cohorts of students have less motivation to succeed than earlier cohorts of students. To assess their concern, they gave a standardized measure of achievement orientation to a random sample of college freshmen in 2009. They compared their achievement orientation scores (which ranged from 0 – 100) to norms of U.S. college freshmen from 2004 who had μ = 85 and σ = 4.

a.

What type of analysis (type of hypothesis test) would you perform to test whether current college freshmen differ from college freshmen in 2004? Justify your answer.

b.

Identify the dependent variable.

c.

What is the scale of measurement for the dependent variable? (nominal, ordinal, interval, or ratio)

17. Given the following numbers below, which measure of central tendency would be more appropriate—mean or median? Justify your answer.

22 37 14 17 27 41 30 13

19 21 29 37 29 20 16 17

34 16 35 80 16 12 24 29

18. For a population with μ = 100 and σ = 20, what is the X value corresponding to z = -0.55?

19. If μ = 400 and σ = 100, what is the probability of selecting at random a score less than or equal to 470?

20. A research wanted to see whether there was a relationship between smoking and residing area so he conducted a survey of 200 people. The results are shown in the following table.

Smoking Habit

Yes

No

Rural

45

55

City

35

65

a.

Fill in the table for the expected counts.

Smoking Habit

Yes

No

Rural

City

b.

Calculate the value of the chi-square statistic.

c.

What are the degrees of freedom?

d.

Do you reject or retain the null hypothesis for α=.05?

e.

What would you conclude? (Note: “I reject/retain the null hypothesis is not sufficient.”)

21. With the growth of cell phone providers, a researcher decides to examine whether there is a correlation between cost of cell phone service per month (rounded to the nearest dollar) and degree of customer satisfaction (on a scale of 1 - 10 with a 1 being not at all satisfied and a 10 being extremely satisfied). The researcher only includes programs with comparable types of services. A sample of the data is provided below.

dollars

satisfaction

41

6

48

8

47

10

45

4

39

9

35

6

42

3

49

5

52

2

55

10

a. What is the Pearson correlation coefficient?

b. Based on the correlation, would you say there is a relationship between cell phone provider price and level of satisfaction? Justify your answer.

Enjoy Your Summer!