2. State whether you would use a two-sample Z test for population means, a match

Question

2. State whether you would use a two-sample Z test for population means, a matched pairs t test, a two-sample t test for population means with equal variances, or a two-sample t test for population means with unequal variances in each of the following scenarios. Give a brief explanation as to why you made your selection: (a) You are the chief statistican for a pharmaceutical company that’s developing a new diabetes drug. You want to measure the mean response to the drug and the mean response to a placebo in order to measure the drug’s effectiveness. In your study, you have split the population into two groups, one obtaining the treatment and one obtaining the placebo, and then formed pairs of one participant from each group using a combination of random assignment and matching based on similar traits. (b) You are the chief statistician for a pharmaceutical company that’s developing a new drug to prevent flea bites in dogs. In particular, your company is interested in how the drug will affect golden retrievers, and specifically if males respond to the drug differently than females. You obtained random samples from a population of male golden retrievers, and a population of female golden retrievers, and computed the sample mean and sample standard deviation from each population. (c) You are a financial analyst, and your company is trying to choose between two investments. The variance of the return of each investment is known, but your company wants to know if either investment has a higher average return. You take a simple random sample of 100 days, and measured the return of the investment on each of those days, which you used to calculate a sample mean for each population. Page 2 (d) You work in the music industry, and are conducting a study for your record label on how recent news has affected different demographics. In your study, you take a simple random sample from a population of men 50 and over, and a simple random sample from a population of girls age 10-15, and measure their response to the question “On a scale of 1-10, how upset are you that Zayn left One Direction?” and computed sample means and sample standard deviations from each population.

Explanation / Answer

2. State whether you would use a two-sample Z test for population means, a matched pairs t test, a two-sample t test for population means with equal variances, or a two-sample t test for population means with unequal variances in each of the following scenarios. Give a brief explanation as to why you made your selection:

A matched pairs t test is used because the subjects are matched on similar traits.

(b) You are the chief statistician for a pharmaceutical company that’s developing a new drug to prevent flea bites in dogs. In particular, your company is interested in how the drug will affect golden retrievers, and specifically if males respond to the drug differently than females. You obtained random samples from a population of male golden retrievers, and a population of female golden retrievers, and computed the sample mean and sample standard deviation from each population.

A two-sample t test for population means with equal variances because we are comparing two independent groups.

(c) You are a financial analyst, and your company is trying to choose between two investments. The variance of the return of each investment is known, but your company wants to know if either investment has a higher average return. You take a simple random sample of 100 days, and measured the return of the investment on each of those days, which you used to calculate a sample mean for each population.

A two-sample Z test for population means because population variation is known.

(d) You work in the music industry, and are conducting a study for your record label on how recent news has affected different demographics. In your study, you take a simple random sample from a population of men 50 and over, and a simple random sample from a population of girls age 10-15, and measure their response to the question “On a scale of 1-10, how upset are you that Zayn left One Direction?” and computed sample means and sample standard deviations from each population.

A two-sample t test for population means with equal variances because we are comparing two independent groups.

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