# Hypothesis Testing, Cohen's d & Effect size

1. A researcher recorded the amount of time each bird spent in the plain chamber during a 60-minute session. Suppose the study produced a mean of M=37 minutes on the plain chamber with SS=288 for a sample of n=9 birds. (Note: If the eye spots have no effect, then the birds should spend an average of µ=30 minutes in each chamber.)

A. Calculate and report the value of the t-statistic. Do you reject or fail to reject the null hypothesis?

B. Compute the estimated Cohen's d.

2. A sample of n=25 children who attend day care before starting school had an average score of M=87 with SS=1536 on a standard math test for which the population mean is µ=81. Use a two-tailed test with α=.01.

A. Calculate and report the value of the t-statistic.

B. Do you reject or fail to reject the null hypothesis?

3. It is known that laboratory rats normally eat an average of µ=21 grams of food each day. Researchers select a random sample of n=16 rats and place them in a controlled atmosphere room in which the relative humidity is maintained at 90%. The daily food consumption scores for the rats are as follows:

14, 18, 21, 15, 18, 18, 21, 18

16, 20, 17, 19, 20, 17, 17, 19

A. What is the value of the t-statistics? Do you reject or fail to reject the null hypothesis?

B. Compute the requested values.

4. An independent-measures research study was used to compare two treatment conditions with n=12 participants in each treatment. The first treatment had a mean of M=55 with a variance of s2 =8, and the second treatment had M=52 and s2=4. Use a two-tailed test with α=.05.

A. What is the value of the t-statistic? Do you reject or fail to reject the null hypothesis?

5. The following results are similar to those obtained in a recent study. The scores are a measure of concern about the negative aspects of eating.

Males Females

N=6 N=9

M=31 M=45

SS=490 SS=680

A. What is the value of the t-statistic? Do you reject or fail to reject the null hypothesis?

B. Compute the value.

6. A researcher conducts an independent-measures research study and obtains t=2.070 with df=28.

A. How many individuals participated in the entire research study?

B. Using a two-tailed test with α=.05, is there a significant difference between the two treatment conditions?

C. Compute r2 to measure the percentage of variance accounted for by the treatment effect.

PLEASE SHOW THE STEPS TO SOLVE EACH PROBLEM.

#### Solution Summary

The solution provides step by step method for the calculation of testing of hypothesis, Cohen's d and effect size. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.