Question

Suppose we have collected times, in minutes, that it takes volunteers to complete a set of pencil and paper mazes. Volunteers are randomly assigned to one of two groups. Group 1 watch a 5 minute video explaining good strategies for completing the mazes. Group 2 watch a 5 minute video of other people successfully completing the mazes, but with no explanation given.

Researchers are interested in testing against the null hypothesis that there is no difference in population mean times that it takes people to complete mazes after watching either type of video.

There are the summary statistics after collecting data. Note that the sample sizes differ, because some subjects did not follow instructions correctly and so they were not included in the analysis.

x₁ = 10.76, x₂ = 9.98
s₁ = 8.78, s₂ = 7.73
n₁ = 46, n₂ = 57

a. Make the following statements true:
This an experimental Observational Experimental study.
Finishing Time is a quantitative variable.
Video Type is a  Categorical variable.
The predictor variable is Video Type and the response variable is  Finishing Time.

b.How should the null hypothesis be written?

H₀: x₁ - x₂ = 0H₀: x₁ - x₂ = 5    H₀: μ₁ - μ₂ = 0H₀: μ = 0H₀: x = 5H₀: μ₁ - μ₂ = 5

(for the following calculations, round to 2 decimal places)
c. Calculate the standard error of x₁ - x₂:

d. Calculate the approximate 95% CI for μ₁ - μ₂:  to

e. The result of the hypothesis test is:
We  --- do not do have evidence that there is a difference in population means, because the null value is  --- outside inside the 95% CI.

f. What kind of error is it *possible* that we have made?
Since we  --- failed to reject rejected the null hypothesis, it is possible that we made a  --- Type I Type II error.

Answer 1