Hypothesis testing using Z statistics:
A researcher is interested in whether short-term memory in the elderly is different from short-term memory in the general population. The literature suggests that short-term memory declines with age. The mean on a short-term memory test for the general population, μ =125, with a standard deviation of σ = 10; the mean for the sample of n =36 people over the age of 80 years is M = 121. Test the hypothesis that the elderly sample has significantly less short-term memory than the general population. Use α = .05
Single sample t-tests:
What critical value of t should be used when you have 20 people in a sample and a nondirectional test is conducted at α = .05?
What critical value of t should be used when you have 20 people in a sample and a directional test is conducted at α = .05?
Patients in a dentist’s office are asked to estimate the total amount of time each day they spend brushing and flossing their teeth. Test whether their average estimates of time is less than the recommended time of μ = 10 minutes. Conduct a single sample t- test at the .05 level of significance. Here are the data (in minutes):
11 13 8 4 9 12 8 5 7 3
Answer the following questions and be sure to show your work.
- What are the null & alternative hypotheses?
- What are the degrees of freedom?
- What is the critical value of t?
- What is the observed value of t?
- What is your decision about the null hypothesis/why?
- If appropriate, calculate Cohen’s d and report its value.
- Write the t statistic using appropriate APA style.
- How would you interpret your findings?
Independent samples t-test:
You want to test whether plants grow better when you talk to them. You obtain two sets of philodendrons, talk to one set and ignore the other (except to water them). After 6 months, you measure their growth in inches. The data are below. Conduct an independent samples ttest with alpha = .05 with a nondirectional test to determine if there was a significant difference between the two sets of plants.
Answer the following questions and be sure to show your work.
- What are the null & alternative hypotheses?
- What are the degrees of freedom?
- What is the critical value of t?
- What is the observed value of t?
- What is your decision about the null hypothesis/why?
- If appropriate, calculate Cohen’s d and report its value.
- Write the t statistic using appropriate APA style.
- How would you interpret your findings?
Not talked to Talked to
4 8
2 7
8 13
4 6
6 5
6 11
3 8
- 9
- 10
You are interested in gender differences in how much money is spent on clothes each month. There were 20 participants in your study, 10 men and 10 women. Their data are shown below. Is there a significant difference between men and women on how much they spend? With alpha = .05, conduct an independent samples t-test to test the hypothesis that genders differ in how much they spend on clothes each month?
Answer the following questions and be sure to show your work.
- What are the null & alternative hypotheses?
- What are the degrees of freedom?
- What is the critical value of t?
- What is the observed value of t?
- What is your decision about the null hypothesis/why?
- If appropriate, calculate Cohen’s d and report its value.
- Write the t statistic using appropriate APA style.
- How would you interpret your findings?
$ Men $ Women
50 150
25 200
35 175 150 300
15 100
75 300
50 165
100 195
80 100
125 50
Related samples t-test
Test whether semester GPA significantly changes during a semester abroad program. Use a related (dependent) samples t-test and alpha = .05 with a nondirectional test. The data are presented below.
Answer the following questions and be sure to show your work.
- What are the null & alternative hypotheses?
- What are the degrees of freedom?
- What is the critical value of t?
- What is the observed value of t?
- What is your decision about the null hypothesis/why?
- If appropriate, calculate Cohen’s d and report its value.
- Write the t statistic using appropriate APA style.
- How would you interpret your findings?
Before program During program
2.94 3.03 2.22 1.79 3.12 3.13 1.99 2.97 3.43 3.75 3.08 3.11 2.81 2.98 3.72 3.92 2.18 2.03
3.60 3.52
A pain clinic asks patients to report their pain on a scale of 0 to 10 before and after acupuncture. Test whether there is a decrease in pain experience using a related samples ttest. Use a related (dependent) samples t-test and alpha = .01 with a directional test. The data appear below.
Answer the following questions and be sure to show your work.
- What are the null & alternative hypotheses?
- What are the degrees of freedom?
- What is the critical value of t?
- What is the observed value of t?
- What is your decision about the null hypothesis/why?
- If appropriate, calculate Cohen’s d and report its value.
- Write the t statistic using appropriate APA style.
- How would you interpret your findings?
Before After
9 7
- 6
- 8
- 7
- 5
8 8
5 4
7 6
