We have covered: One-sample t-test, matched pairs t-test, sign test, 2 sample t-

Question

We have covered: One-sample t-test, matched pairs t-test, sign test, 2 sample t-test, rank sum test, ANOVA F-test, and simple linear regression.

Suggest one of the above methods that would be appropriate in the scenarios below, though more than one method may be appropriate:

Scenario 1.

I am looking at several different cities in the state of Connecticut. I wish to determine whether there is a significant difference in the mean yearly number of violent crimes among the cities. What testing procedure would help to answer this question – why?

Scenario 2.

I wish to determine whether city income is associated with the number of violent crimes in a city. What testing procedure would help to answer this question – why?

Scenario 3.

I’m interested in estimating the mean number of people who pull out in front of me without stopping on my commute to UCONN. I record 20 trips to campus, and find that an average of 3.6 people per trip pull out. I’d like to test the hypothesis that the mean number of people pulling out is greater than 3 people per trip.

Scenario 4.

The Ohio Dairymen’s Association is incensed by California’s recent ad campaign, and wishes to determine if happy cows really do come from California. They decide to measure this by recording the number of “moos per cow per hour” of 30 randomly selected herds in California, and do the same for 35 randomly selected herds in Ohio. They would like to compare the mean number of moos per cow per hour for California cows and Ohio cows.

Scenario 5.

A researcher wants to test the claim that runners who train for a marathon with a partner run significantly faster than those who train for a marathon on their own. Only runners who finished the marathon within 12 hours had an average speed recorded; anyone who took longer than this was recorded as ‘did not finish’. What statistical procedure would test his claim - why?

Explanation / Answer

Scenario1:

Here we want to compare more than 2 population means so ANOVA F test will be used.

Scenario 2:

Here we want to determine whether city income and the number of violent crimes in a city are related to each other or not. So simple linear regression will be used.

Scenario 3:

Here we have single sample and we wnat to compare single population mean so single sample t test will be used.

Scenario 4:

Here we have two independent samples:

sample 1: 30 randomly selected herds in California

sample 2: 35 randomly selected herds in Ohio

And we want ot compare mean number of moos per cow per hour for California cows and Ohio cows (mean of two popaultions) so independent sample t test wil be used.

Scenario 5:

Here we have two independent samples so  independent sample t test wil be used.

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