Two-sample Problems

BPS chapter 18

© 2010 W.H. Freeman and Company

Type of scenario A university professor wanted to know if the attitudes towards statistics

changed during the course of the semester. She took a simple random sample of students and gave them a test at the beginning of the term to assess their feelings toward statistics. When the semester was finished she administered another test to the same group of students and wanted to see if there was a difference between the average attitude towards statistics.

What type of scenario is this?

a) Matched pairs

b) Two independent samples

Type of scenario (answer)A university professor wanted to know if the attitudes towards statistics

changed during the course of the semester. She took a simple random sample of students and gave them a test at the beginning of the term to assess their feelings toward statistics. When the semester was finished she administered another test to the same group of students and wanted to see if there was a difference between the average attitude towards statistics.

What type of scenario is this?

a) Matched pairs

b) Two independent samples

Type of scenario The National Park Service is interested in comparing the amount of

money that visitors in two different national parks spend. They sample visitors on the same day in each of the two parks and then compare the mean dollar amounts spent from each sample.

What type of scenario is this?

a) Matched pairs

b) Two independent samples

Type of scenario (answer)The National Park Service is interested in comparing the amount of

money that visitors in two different national parks spend. They sample visitors on the same day in each of the two parks and then compare the mean dollar amounts spent from each sample.

What type of scenario is this?

a) Matched pairs

b) Two independent samples

Type of scenario Researchers at a pharmaceutical company were developing a new

formula for their sunscreen. They wanted to see if the new formula provided better protection against sunburns than the formula that was already on the market. They applied the new formula to one arm of an individual and the old formula to the other arm, randomly choosing the arms for each formula. Then they compared the color difference between the arms.

What type of scenario is this?

a) Matched pairs

b) Two independent samples

Type of scenario (answer)Researchers at a pharmaceutical company were developing a new

formula for their sunscreen. They wanted to see if the new formula provided better protection against sunburns than the formula that was already on the market. They applied the new formula to one arm of an individual and the old formula to the other arm, randomly choosing the arms for each formula. Then they compared the color difference between the arms.

What type of scenario is this?

a) Matched pairs

b) Two independent samples

Type of scenario A group of psychologists was interested in knowing if the living

environment had any effect on a student’s GPA. They took a set of twins and randomly assigned one twin to live in an urban area and the other twin to live in a rural area. After one year, they computed the GPAs for the twins and looked at the differences.

What type of scenario is this?

a) Matched pairs

b) Two independent samples

Type of scenario (answer) A group of psychologists was interested in knowing if the living

environment had any effect on a student’s GPA. They took a set of twins and randomly assigned one twin to live in an urban area and the other twin to live in a rural area. After one year, they computed the GPAs for the twins and looked at the differences.

What type of scenario is this?

a) Matched pairs

b) Two independent samples

Matched pairs hypotheses A group of psychologists was interested in knowing if the living

environment had any effect on a student’s GPA. They took a set of twins and randomly assigned one twin to live in an urban area and the other twin to live in a rural area. After one year, they computed the GPAs for the twins and looked at the differences.

What are the hypotheses of interest?

a)

b)

c)

d)

Matched pairs hypotheses (answer) A group of psychologists was interested in knowing if the living

environment had any effect on a student’s GPA. They took a set of twins and randomly assigned one twin to live in an urban area and the other twin to live in a rural area. After one year, they computed the GPAs for the twins and looked at the differences.

What are the hypotheses of interest?

a)

b)

c)

d)

Matched pairs hypotheses A group of psychologists was interested in knowing if the living

environment had any effect on a student’s GPA. They took a set of twins and randomly assigned one twin to live in an urban area and the other twin to live in a rural area. After one year, they computed the GPAs for the twins and looked at the differences.

The P-value was found to be between 0.20 and 0.25. What can you conclude if = 0.05?

a) Reject H0 and say that a difference exists between the mean GPAs.

b) Reject H0 and say there is insufficient evidence to say that a difference exists between the mean GPAs.

c) Do not reject H0 and say that a difference exists between the mean GPAs.

d) Do not reject H0 and say there is insufficient evidence to say that a difference exists between the mean GPAs.

Matched pairs hypotheses (answer)A group of psychologists was interested in knowing if the living

environment had any effect on a student’s GPA. They took a set of twins and randomly assigned one twin to live in an urban area and the other twin to live in a rural area. After one year, they computed the GPAs for the twins and looked at the differences.

The P-value was found to be between 0.20 and 0.25. What can you conclude if = 0.05?

a) Reject H0 and say that a difference exists between the mean GPAs.

b) Reject H0 and say there is insufficient evidence to say that a difference exists between the mean GPAs.

c) Do not reject H0 and say that a difference exists between the mean GPAs.

d) Do not reject H0 and say there is insufficient evidence to say that a difference exists between the mean GPAs.

Matched pairs hypotheses A group of psychologists was interested in knowing if the living

environment had any effect on a student’s GPA. They took a set of twins and randomly assigned one twin to live in an urban area and the other twin to live in a rural area. After one year, they computed the GPAs for the twins and looked at the differences.

The psychologists calculated a 95% confidence interval for d to be (-0.066, 0.146). Which one of the following shows a correct interpretation of this interval?

a) We are 95% confident that the mean GPA is somewhere in this interval.

b) 95% of the GPAs are found in that interval.

c) We are 95% confident that the mean difference between GPAs is in the interval.

d) 95% of the differences in GPAs can be found in the interval.

Matched pairs hypotheses (answer)A group of psychologists was interested in knowing if the living

environment had any effect on a student’s GPA. They took a set of twins and randomly assigned one twin to live in an urban area and the other twin to live in a rural area. After one year, they computed the GPAs for the twins and looked at the differences.

The psychologists calculated a 95% confidence interval for d to be (-0.066, 0.146). Which one of the following shows a correct interpretation of this interval?

a) We are 95% confident that the mean GPA is somewhere in this interval.

b) 95% of the GPAs are found in that interval.

c) We are 95% confident that the mean difference between GPAs is in the interval.

d) 95% of the differences in GPAs can be found in the interval.

Type of scenario An experiment was conducted to see if elderly patients had more

trouble keeping their balance when loud, unpredictable noises were made compared to younger patients who were also exposed to the noises. Researchers compared the amount of forward and backward sway for the two groups.

This is an example of a

a) Matched pairs experiment because we are analyzing the mean difference between the elderly and the young.

b) Matched pairs experiment because we have two sets of data.

c) Two-sample t-test because the two groups were both exposed to the noises.

d) Two-sample t-test because the two groups are independent from one another.

Type of scenario (answer)An experiment was conducted to see if elderly patients had more

trouble keeping their balance when loud, unpredictable noises were made compared to younger patients who were also exposed to the noises. Researchers compared the amount of forward and backward sway for the two groups.

This is an example of a

a) Matched pairs experiment because we are analyzing the mean difference between the elderly and the young.

b) Matched pairs experiment because we have two sets of data.

c) Two-sample t-test because the two groups were both exposed to the noises.

d) Two-sample t-test because the two groups are independent from one another.

Parameter of interest An experiment was conducted to see if elderly patients had more

trouble keeping their balance when loud, unpredictable noises were made compared to younger patients who were also exposed to the noises. Researchers compared the amount of forward and backward sway for the two groups.

What is the best parameter of interest when comparing the means of two groups?

a)

b)

c)

d)

Parameter of interest (answer)An experiment was conducted to see if elderly patients had more

trouble keeping their balance when loud, unpredictable noises were made compared to younger patients who were also exposed to the noises. Researchers compared the amount of forward and backward sway for the two groups.

What is the best parameter of interest when comparing the means of two groups?

a)

b)

c)

d)

Hypotheses An experiment was conducted to see if elderly patients had more

trouble keeping their balance when loud, unpredictable noises were made compared to younger patients who were also exposed to the noises. Researchers compared the amount of forward and backward sway for the two groups.

If we wanted to test whether the younger patients had less average forward/backward sway, we would use which of the following hypotheses?

a)

b)

c)

d)

Hypotheses (answer) An experiment was conducted to see if elderly patients had more

trouble keeping their balance when loud, unpredictable noises were made compared to younger patients who were also exposed to the noises. Researchers compared the amount of forward and backward sway for the two groups.

If we wanted to test whether the younger patients had less average forward/backward sway, we would use which of the following hypotheses?

a)

b)

c)

d)