Question

Note: EVERY time you perform a calculation, show the formula, numbers plugged in, and final answer.

#1. Twelve participants completed a mood assessment, then watched a funny video clip, and repeated the mood

assessment. Lower values on the assessment indicate better mood. A difference score was calculated for each

individual: score after – score before, so if mood improved (mood score drops as a result of watching the funny

video) we would expect the difference to be a negative value. The mean of all 12 difference scores = -2.417 with a

standard deviation of 1.24. Conduct a formal test of hypothesis (a = 0.05) to see whether watching funny videos

caused a change in mood.

Mean of the difference scores (M) _____ Standard deviation of the difference scores = ______ Sample size (N) _____

STEP 1. Identify the two populations we are comparing

Population 1: Population 2:

STEP 2. Hypotheses in words and symbols

Null:

Research:

STEP 3. Characteristics of the comparison distribution.

Label the distribution with standard error values from -3 to +3 à

µM = 0 (ALWAYS 0 FOR PAIRED-SAMPLES t TESTS)

sM =

Note: EVERY time you perform a calculation, show the formula, numbers plugged in, and final answer.

#1. Twelve participants completed a mood assessment, then watched a funny video clip, and repeated the mood

assessment. Lower values on the assessment indicate better mood. A difference score was calculated for each

individual: score after – score before, so if mood improved (mood score drops as a result of watching the funny

video) we would expect the difference to be a negative value. The mean of all 12 difference scores = -2.417 with a

standard deviation of 1.24. Conduct a formal test of hypothesis (a = 0.05) to see whether watching funny videos

caused a change in mood.

Mean of the difference scores (M) _____ Standard deviation of the difference scores = ______ Sample size (N) _____

STEP 1. Identify the two populations we are comparing

Population 1: Population 2:

STEP 2. Hypotheses in words and symbols

Null:

Research:

STEP 3. Characteristics of the comparison distribution.

Label the distribution with standard error values from -3 to +3 à

µM = 0 (ALWAYS 0 FOR PAIRED-SAMPLES t TESTS)

sM =

STEP 4. Critical values for a p level = 0.05 are _________

Label the critical values on the distribution and shade the rejection regions.

STEP 5. Calculate the test statistic and mark it on the comparison distribution

STEP 6. Write the results in APA format [ t(df) = test statistic, p < __ ] and write your hypothesis-testing conclusion

in words in terms of this problem.

1If the sample mean was not an accurate estimate of the mean of the population from which it was drawn, you might have

made an error – Type I or Type II. State which error you might have made based on your hypothesis testing conclusion AND

what the error would be in words in terms of this problem.

Calculate effect size and state whether the effect is non-existent, small, moderate, or large.

Calculate a 95% confidence interval to estimate the mean difference of the entire population – change in mood as

a result of watching funny videos:

What is the value of alpha?

What critical value(s) will you use:

Calculate standard error and then the confidence interval of the difference:

Interpret your confidence interval estimate of the difference between conditions AND state whether or not you

would reject the null hypothesis based on the CI you’ve calculated (just say “reject” or “do not reject”) and explain

how you came to your decision.

23

#2. Many communities worldwide are lamenting the effects of so-called big box retailers (e.g., Walmart) on their

local economies, particularly on small, independently owned shops. Do these large stores reduce earnings of

locally owned retailers? Imagine that you decide to test this premise. You assess earnings at 20 local stores for the

month of October, a few months before a big box store opens. You then assess earnings the following October,

correcting for inflation. A difference score was calculated for each individual store: earnings after – earnings

before. If one store earned only $1,800 after and had earned $2,400 before, then that store’s difference score

would be -600.00. If presence of the Walmart reduced earnings for most local stores in our sample we would

expect to see negative mean difference score. Conduct a formal test of hypothesis (a = 0.01) to see whether the

presence of a large store reduces income for locally owned retailers.

Mean of the difference scores (M) = -804.64 Standard deviation of the difference scores, s = 292.55 Sample size (N) _____ a = _____

STEP 1. Identify the two populations we are comparing

Population 1: Population 2:

STEP 2. Hypotheses in words and symbols

Null:

Research:

STEP 3. Characteristics of the comparison distribution.

Label the distribution with standard error values from -3 to +3 à

µM = 0 (ALWAYS 0 FOR PAIRED-SAMPLES t TESTS)

sM =

STEP 4. Critical values for a p level = 0.01 are _________

Label the critical values on the distribution and shade the rejection regions.

STEP 5. Calculate the test statistic and mark it on the comparison distribution

STEP 6. Write the results in APA format [ t(df) = test statistic, p < __ ] and write your hypothesis-testing conclusion

in words in terms of this problem. If the sample mean was not an accurate estimate of the mean of the population from which it was drawn, you might have

made an error – Type I or Type II. State which error you might have made based on your hypothesis testing conclusion AND

what the error would be in words in terms of this problem.

Calculate effect size and state whether the effect is non-existent, small, moderate, or large.

Calculate a 99% confidence interval to estimate the mean difference of the entire population:

What is the value of alpha?

What critical value(s) will you use:

Calculate standard error and then the confidence interval of the difference:

Interpret your confidence interval estimate of the difference between conditions AND state whether or not you

would reject the null hypothesis based on the CI you’ve calculated (just say “reject” or “do not reject”) and explain

how you came to your decision.

STEP 4. Critical values for a p level = 0.05 are _________

Label the critical values on the distribution and shade the rejection regions.

STEP 5. Calculate the test statistic and mark it on the comparison distribution

STEP 6. Write the results in APA format [ t(df) = test statistic, p < __ ] and write your hypothesis-testing conclusion

in words in terms of this problem.

1If the sample mean was not an accurate estimate of the mean of the population from which it was drawn, you might have

made an error – Type I or Type II. State which error you might have made based on your hypothesis testing conclusion AND

what the error would be in words in terms of this problem.

Calculate effect size and state whether the effect is non-existent, small, moderate, or large.

Calculate a 95% confidence interval to estimate the mean difference of the entire population – change in mood as

a result of watching funny videos:

What is the value of alpha?

What critical value(s) will you use:

Calculate standard error and then the confidence interval of the difference:

Interpret your confidence interval estimate of the difference between conditions AND state whether or not you

would reject the null hypothesis based on the CI you’ve calculated (just say “reject” or “do not reject”) and explain

how you came to your decision.

23

#2. Many communities worldwide are lamenting the effects of so-called big box retailers (e.g., Walmart) on their

local economies, particularly on small, independently owned shops. Do these large stores reduce earnings of

locally owned retailers? Imagine that you decide to test this premise. You assess earnings at 20 local stores for the

month of October, a few months before a big box store opens. You then assess earnings the following October,

correcting for inflation. A difference score was calculated for each individual store: earnings after – earnings

before. If one store earned only $1,800 after and had earned $2,400 before, then that store’s difference score

would be -600.00. If presence of the Walmart reduced earnings for most local stores in our sample we would

expect to see negative mean difference score. Conduct a formal test of hypothesis (a = 0.01) to see whether the

presence of a large store reduces income for locally owned retailers.

Mean of the difference scores (M) = -804.64 Standard deviation of the difference scores, s = 292.55 Sample size (N) _____ a = _____

STEP 1. Identify the two populations we are comparing

Population 1: Population 2:

STEP 2. Hypotheses in words and symbols

Null:

Research:

STEP 3. Characteristics of the comparison distribution.

Label the distribution with standard error values from -3 to +3 à

µM = 0 (ALWAYS 0 FOR PAIRED-SAMPLES t TESTS)

sM =

STEP 4. Critical values for a p level = 0.01 are _________

Label the critical values on the distribution and shade the rejection regions.

STEP 5. Calculate the test statistic and mark it on the comparison distribution

STEP 6. Write the results in APA format [ t(df) = test statistic, p < __ ] and write your hypothesis-testing conclusion

in words in terms of this problem. If the sample mean was not an accurate estimate of the mean of the population from which it was drawn, you might have

made an error – Type I or Type II. State which error you might have made based on your hypothesis testing conclusion AND

what the error would be in words in terms of this problem.

Calculate effect size and state whether the effect is non-existent, small, moderate, or large.

Calculate a 99% confidence interval to estimate the mean difference of the entire population:

What is the value of alpha?

What critical value(s) will you use:

Calculate standard error and then the confidence interval of the difference:

Interpret your confidence interval estimate of the difference between conditions AND state whether or not you

would reject the null hypothesis based on the CI you’ve calculated (just say “reject” or “do not reject”) and explain

how you came to your decision.

Answer 1

#1.

Mean of the difference scores (M) =-2.417 Standard deviation of the difference scores (s)= 1.24 Sample size (N) =12

STEP 1.

Population 1: Participants before watching funny video, Population 2: Same Participants after watching funny video

STEP 2.

Research:

STEP 3.

STEP 4. Critical values for a p level = 0.05 are t_0.025,11= 2.2010 and t_0.975,12=-2.2010.

If the sample mean was not an accurate estimate of the mean of the population from which it was drawn, we might have

made an error – Type I since we reject H₀ on the basis of sample.

#2.

Mean of the difference scores (M) = -804.64 Standard deviation of the difference scores (s)= 292.55 Sample size (N) = 20, a=0.01.

STEP 1.

Population 1: locally owned retailers before earning, Population 2: locally owned retailers after earning

STEP 2.

There is sufficient evidence that store’s difference average score differs from -600.00.

If the sample mean was not an accurate estimate of the mean of the population from which it was drawn, we might have

made an error – Type I since we reject H₀ on the basis of sample.

Effect size=|(-804.64+600)/ 292.55| =0.70 so effect size is moderate.

95% CI to estimate the mean difference of the entire population:

( -991.7892, -617.4908)

value of alpha=0.01

critical value(s) that we will use= - 2.8609, 2.8609

We are 99% confident that mean difference of the entire population lies in the interval ( -991.7892, -617.4908). Since this interval does not contain -600 so we reject H₀.