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# Statistics

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Q1) Independent-Samples t Test (25 points total)
A psychologist would like to evaluate the effectiveness of alunchtime walking programon job satisfaction. The psychologist conducted a small study to examine the potential effect of the 6-weeklunchtime walking program on job satisfaction as measured on a 10-item scale at the end of the program.A composite score ranging from 0 to 10 was computed from the scale for each subject with 10 indicating the highest level of job satisfaction. The psychologist recruited 10employees to participate in lunchtime walking program and 12employees with similar demographics who do not participate in the lunchtime walking program. The data are listed in the table below. The psychologist strongly suspects based on prior research that job satisfaction scores will rise as a result of the walking program.The alpha level is set at .05 for the hypothesis test.

Lunchtime walking program No lunchtime walking program
Subject ID # Job satisfaction score Subject ID # Job satisfaction score
1 7 11 5
2 5 12 8
3 8 13 6
4 6 14 5
5 5 15 7
6 9 16 8
7 8 17 6
8 8 18 7
9 6 19 9
10 6 20 6
21 7
22 5

What is the dependent (outcome) variable? What is the independent (grouping) variable? (1 point total: .5 for each variable)

Create the null and alternative hypotheses for this study, using both words and symbol notation.(2 points total: 1 per hypothesis- .5 for written format, .5 for notation)

Calculate M1 andM2.(2 points total: 1 point per sample mean- .5 for work, .5 for answer)

Calculate df1 , df2, and dftotal.(2 points total: 1 for df1 and df2, 1 for total df, including work)

Calculate s21 and s22. (estimated variance for population 1 and variance for population 2) (4 points total: 2 points for each variance. 1 for work and 1 for result)

Calculate the pooled variance for the two populations.(2 points total: 1 point for work, 1 point for result)

Use the pooled variance to calculate the variance for sampling distribution 1 and the variance for sampling distribution 2.(2 points total: 1 for work and 1 for result)

Hint: Sampling distribution derives from the original population and it consists of means of all possible samples drawn from the original population.

Calculate standard deviation of the comparison distribution.(2 points total: 1 for work and 1 for result)

Hint: This is the distribution consisting of differences between means and its standard deviation is the denominator of the t statistic formula.

Calculate the t statistic.(2 points total: 1 for work and 1 for result)

Considering the research question and the hypotheses, should the test be one-tailed or two-tailed? Why? (2 points total: 1 for each answer)

Determine the critical t value(s) for this hypothesis test based on the degree of freedom, from (d), and the preset alpha level. (1 point total)

Compare the calculated t statistic with the critical t value by stating which is more “extreme”, and then make a decision about the hypothesis test by stating clearly “reject” or “fail to reject” the null hypothesis.(1 point total: .5 for comparison, .5 for decision)

Calculate the pooled standard deviation for the populations and then use it to calculate the standardized effect size of this test. (2 point total: 1 for pooled standard deviation, 1 for effect size. Deduct .5 if a result is wrong but the process is correct.)

Q2) Independent-Samples t-Test (25 points total)
A psychologist is interested in understanding the effect of nightly meditation on hours of sleep. The subjects in one group participated in meditation for 20 minutes a night for six weeks. Subjects in the other group did not engage in any nightly meditation.Participants’ sleep was measured with the use of a sleep tracker worn on the wrist. The researcherwould like to run a hypothesis test with α = .05to see if there is a significant difference in sleep hours betweenthose who engaged in nightly meditation and those who did not. The psychologist does not predict whether those who meditate will sleep more or less hours on average, but rather is interested in any direction of the difference.

Meditation program No meditation program,
Participant Average sleep hours Participant Average sleep hours
1 4 11 5
2 7 12 7
3 6 13 8
4 9 14 7
5 7 15 6
6 6 16 6
7 8 17 4
8 9 18 9
9 7 19 7
10 6 20 6

What is the dependent (outcome) variable? What is the independent (grouping) variable? (1 points total: .5 per variable)

Create the null and alternative hypotheses for this study, using both words and symbol notation.(2 points total: 1 per hypothesis- .5 for written format, .5 for notation)

Calculate M1 andM2.(2 points total: 1 point per sample mean- .5 for work, .5 for answer)

Calculate df1 , df2, and dftotal.(2 points total: 1 for df1 and df2 which are the same, 1 for total df, including work)

Calculate s21 and s22. (estimated variance for population 1 and variance for population 2) (4 points total: 2 points for each variance. 1 for work and 1 for result)

Calculate the pooled variance for the two populations.(2 points total: 1 point for work, 1 point for result)

Use the pooled variance to calculate the variance for sampling distribution 1 and the variance for sampling distribution 2.(2 points total: 1 for work and 1 for result)

Hint: Sampling distribution derives from the original population and it consists of means of all possible samples drawn from the original population.

Calculate standard deviation of the comparison distribution.(2 points total: 1 for work and 1 for result)
Hint: This is the distribution consisting of differences between means and its standard deviation is the denominator of the t statistic formula.

Calculate the t statistic.(2 points total: 1 for work and 1 for result)

Considering the research question and the hypotheses, should the test be one-tailed or two-tailed? Why? (2 points total: 1 for each answer)

Determine the critical t value(s) for this hypothesis test based on the degree of freedom, from (d), and the preset alpha level. (1 point total)

Compare the calculated t statistic with the critical t value by stating which is more “extreme”, and then make a decision about the hypothesis test by stating clearly “reject” or “fail to reject” the null hypothesis.(1 point total: .5 for comparison, .5 for decision)

Calculate the pooled standard deviation for the populations and then use it to calculate the standardized effect size of this test. (2 point total: 1 for pooled standard deviation, 1 for effect size. Deduct .5 if a result is wrong but the process is correct.) ### Calculator

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