# Note: EVERY time you perform a

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

**#1.** Twelve participants completed a moodassessment, then watched a funny video clip, and repeated themood

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*) _____ Standarddeviation 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 +3à

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

sM =

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

**#1.** Twelve participants completed a moodassessment, then watched a funny video clip, and repeated themood

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*) _____ Standarddeviation 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 +3à

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 therejection regions.

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

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

in words in terms of this problem.

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

made an error – Type I or Type II. State which error you mighthave 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 isnon-existent, small, moderate, or large.

Calculate a 95% confidence interval to estimate the meandifference 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 thedifference:

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

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

how you came to your decision.

23

**#2.** Many communities worldwide are lamentingthe effects of so-called big box retailers (e.g., Walmart) ontheir

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

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

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

correcting for inflation. A difference score was calculated foreach 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 earningsfor most local stores in our sample we would

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

presence of a large store reduces income for locally ownedretailers.

Mean of the difference scores (*M*) = -804.64 Standarddeviation 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 +3à

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 therejection regions.

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

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

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

made an error – Type I or Type II. State which error you mighthave 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 isnon-existent, small, moderate, or large.

Calculate a 99% confidence interval to estimate the meandifference 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 thedifference:

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

would reject the null hypothesis based on the CI you’vecalculated (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 therejection regions.

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

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

in words in terms of this problem.

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

made an error – Type I or Type II. State which error you mighthave 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 isnon-existent, small, moderate, or large.

Calculate a 95% confidence interval to estimate the meandifference 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 thedifference:

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

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

how you came to your decision.

23

**#2.** Many communities worldwide are lamentingthe effects of so-called big box retailers (e.g., Walmart) ontheir

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

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

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

correcting for inflation. A difference score was calculated foreach 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 earningsfor most local stores in our sample we would

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

presence of a large store reduces income for locally ownedretailers.

Mean of the difference scores (*M*) = -804.64 Standarddeviation 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 +3à

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 therejection regions.

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

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

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

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

Calculate a 99% confidence interval to estimate the meandifference 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 thedifference:

how you came to your decision.

Answer:

**#1.**

Mean of the difference scores (M) =-2.417 Standard deviation ofthe 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 aret_{0.025,11}= 2.2010 and t_{0.975,12}=-2.2010.

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

made an error – Type I since we reject H_{0} on thebasis of sample.

**#2.**

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

STEP 1.

Population 1: locally owned retailers before earning, Population2: locally owned retailers after earning

STEP 2.

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

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

made an error – Type I since we reject H_{0} on thebasis of sample.

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

95% CI to estimate the mean difference of the entirepopulation:

( -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 entirepopulation lies in the interval ( -991.7892, -617.4908). Since thisinterval does not contain -600 so we reject H_{0}.