Question

1. Researchers want to know if there is a relationship between commute time and commute distance in the population of all Atlanta commuters. They collected data from a sample of 500 Atlanta commuters and computed a correlation of r = 0.807 between commute time and commute distance. StatKey was used to construct a 95% confidence interval of [0.725, 0.867] for the population correlation.

A. If researchers wanted to conduct a hypothesis test to determine if there is a relationship commute time and commute distance in the population of all Atlanta commuters, what hypotheses would they test? State the null and alternative hypotheses using appropriate symbols.

If the hypotheses from part A were tested, would you expect the p value to be less than or greater than 0.05? Explain why.

(Hint: Apply the 95% confidence interval given in the scenario)

2.

Research question: Is the average monthly rent of a two-bedroom apartment in Manhattan different from $5000?

Data were collected from a random sample of 41 two-bedroom apartments in Manhattan. The mean rental rate was $5563.77 with a standard deviation of $4586.51. The distribution was strongly skewed to the right. StatKey was used to conduct a randomization test and a p value of 0.414 was computed for the two-tailed test.

A. In order to increase statistical power should the researchers obtain a larger or smaller sample size?

In addition to changing the sample size, as in part A, what is one additional realistic change that could be made in future studies to increase the statistical power of this test?

Answer 1