Reference no: EM132465138
A researcher is interested in understanding the effect of college education on wages. The workers in one group have earned an AA (associate's) degree while members of the other group hold at least a bachelor's degree. The researcher would like to run a hypothesis test with α = .05 to see if those with a bachelor's degree have significantly higher hourly wages than those with an associate's degree.
Bachelor's degree
Participant Hourly wage
1 13.25
2 12.25
3 11.60
4 9.80
5 9.40
6 12.60
7 11.80
8 11.50
9 11.90
10 12.70
Associate's degree
Participant Hourly wage
11 10.25
12 11.25
13 9.25
14 11.75
15 9.70
16 11.00
17 10.00
18 9.40
19 9.20
20 10.20
a) What is the dependent (outcome) variable? What is the independent (grouping) variable? (1 points total: .5 per variable)
b) 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)
c) Calculate M1 and M2 (2 points total: 1 point per sample mean- .5 for work, .5 for answer)
d) Calculate df1 , df2, and dftotal (2 points total: 1 for df1 and df2 which are the same, 1 for total df, including work)
e) Calculate 21 and 22 (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)
f) Calculate the pooled variance for the two populations (2 points total: 1 point for work, 1 point for result)
g) 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.
h) 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.
i) Calculate the t statistic (2 points total: 1 for work and 1 for result)
j) Considering the research question and the hypotheses, should the test be one-tailed or two-tailed? Why? (2 points total: 1 for each answer)
k) 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)
l) 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)
m) 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.)