Question

A researcher wanted to see whether there was a difference between NYC citizens and Boston citizens in the amount of time (in hours) they spent outside during April 2020. He collected two samples – one of NYC citizens and the other of Boston citizens, and measured the amount of time each subject spent outside during April 2020. Sample #1 (of NYC citizens) contained 24 subjects (n₁=24), the mean number of hours spent outside was M₁=40, and the sample’s variance was S₁²=64. Sample #2 (of Boston citizens) contained 24 subjects (n₂=24), the mean number of hours spent outside was M₂=28, and the sample’s variance was S₂²=25.

a. Which test should be used to analyze your data? Explain your answer. (3 points)

b. Conduct the appropriate nondirectional hypothesis test on these data. Use α=0.05. You must submit your calculations (if you do not submit your calculations, you will lose points). (8 points)

c. Calculate the appropriate effect size measure. You must submit your calculations (if you do not submit your calculations, you will lose points). (4 points)

d. Compute a 95% confidence interval for the mean difference. You must submit your calculations (if you do not submit your calculations, you will lose points). (5 points)

Answer 1

Answer:

a)

T-test for 2 means with Unknown standard deviation

b)

c)

Difference in sample means =    x̅1-x̅2 =    40.0000   -   28.0   =   12.00

Pooled std dev, Sp=   √ ([(n1 - 1) s1² + (n2 - 1) s2²]/ (n1+n2-2))

                             = 48.585

Effect size

Cohen’s d =    |( x̅1-x̅2 )/Sp |

                      =    0.247

d)