Researchers wanted to examine the effects of the intensity of physical activity on a scale of positive mood.People who engage in moderate-low intensity of physical activity for 3 hours per week have a mean of μ = 40 on the positive mood scale, with a standard deviation of σ = 8.
A) Would this be a one- or two-tailed test? Why?
B) State the null and alternative hypotheses (H0 and H1) based on your answer to A.
C) What is the critical z-score that would infer that the sample mean is statistically different from the population mean using alpha = .05?
They took a sample of n = 30 participants from this population, and asked them to exercise at moderate-high physical intensity for a month (they exercised for the same amount of time per week). After the month of moderate-high intensity exercise, this sample had a mean of M = 44 on the mood scale.
D) Does this sample provide enough evidence to conclude that moderate-high intensity exercisers are significantly different in mood from the moderate-low exercisers? Test this.
E) Compute either Cohen's d or η2 to measure the size of the difference. Explain what this means in plain English.
F) If the population standard deviation is σ = 12, does the sample still significantly differ from the population?Use the two-tailed test with α = .05.
G) How does the difference in standard deviation influence the outcome of the hypothesis test?
Researchers are investigating sleeping habits of young adults in order to determine if they currently get more, less, or the same amount of sleep compared to young adults in the 1970s.
The sample of n = 20 young adults reported getting an average of 6.7 hours of sleep with SS = 24. In the 1970s, young adults got an average of μ = 7.4 hours of sleep.
A) State the null and alternative hypothesis.
B) What are the critical values given an α = .05?
C) Test the null hypothesis that current young adults do not get more or less sleep than adults in the 1970s (μ = 7.4) with α = .05. In other words, do young adults currently differ in length of sleeps than young adults from the 1970s? Conduct your t-test.
D) State your findings in plain English based on the results of your hypothesis test.
A farmer is trying to determine how fertile his plots of land are for growing wheat. The average number of bushels of wheat per acre is μ = 80. The farmer counts how many bushels he collects from n = 10 acres of his land. The number of bushels per acre are as follows: 92, 79, 86, 74, 96, 82, 76, 87, 93, 84.
Conduct a t-test from start to finish.
On the basis of this sample, does this farmer's harvest differ from the population at an alpha level of α = .01?
Compute the estimated Cohen's d to measure the size of the difference.
Explain the findings of your t-test and Cohen's d in plain English.