US commuters

A recent survey of US commuters found that their daily one-way commute time averages 50 minutes with a standard deviation of 15 minutes. An investigator wishes to determine whether the national mean commute time describes the mean commute time for all workers in the New York City area. Commute times are obtained for a random sample of 225 workers from this area, and the mean time is found to be 65 minutes. Test the null hypothesis with z, at the .05 level of significance.

(2 points each)

What are the statistical hypotheses (H0 and H1)?
What is the decision rule (based on the specified .05 level of significance)?
Calculate the z ratio.
What is your final decision with respect to H0?
Interpret the final decision.



A recent survey found that dog owners were happier than cat owners, with nearly twice the amount of dog owners reporting that they were “very happy” compared to cat owners. A researcher decides to further investigate this finding by conducting a study where 16 subjects are randomly assigned to either play with a puppy for one hour, or to play with a kitten for one hour. At the end of the one hour period, a blood sample is taken from each subject to measure their endorphin levels (a body hormone that can induce feelings of happiness). The results from the study are below:

Puppy Group: 13, 19, 14, 17, 10, 20, 19
Kitten Group: 14, 11, 7, 8, 7, 9, 11
Test the null hypothesis with t, at the .01 level of significance:

(2 points each)

What are the statistical hypotheses (H0 and H1)?
What is the decision rule (at the specified .01 level of significance)?
Calculate the t ratio.
What is your final decision with respect to H0?
Interpret the final decision.

A beverage company is testing two competing vitamin-D enhanced iced tea beverages they are currently developing, Immuni-T and BoosT, in order to determine which product should be introduced into the market. The company arranges for a independent lab to compare the vitamin D levels in 12 subjects, evenly divided among three groups: one group that consumes 16 ounces of filtered water, one group that consumes 16 ounces of Immuni-T, and one group that consumes 16 ounces of BoosT. All subjects rest for 30 minutes before submitting a blood sample for measurement. The results of the test are below:

Filtered water: 5, 7, 4, 8
Immuni-T: 12, 10, 11, 10
BoosT: 10, 9, 11, 10
Conduct a one-way analysis of variance, at the .01 level of significance:

What are the statistical hypotheses (H0 and H1)?
What is the decision rule (at the specified .01 level of significance)?
Calculate the F ratio.
What is your final decision with respect to H0?

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