1. Suppose a geologist wants to investigate the claim that the mean time between eruptions (in minutes) of a certain geyser in Yellowstone National Park has decreased over the past 20 years. If the times between eruptions observed in the recent past are defined as Population 1 and the times between eruptions measured 20 years ago are defined as Population 2. what are the symbolic forms ol the null and alternative hypotheses needed to lest the geologist’s claim?

2. To perform the hypothesis test in Question 1, the geologist observes the times between randomly selected pairs of eruptions over a period of roughly one month, then obtains similar data for eruptions from 20 years ago from a data archive. The StatCrunch data set for this exercise contains one column for the recent observations (“Recent”) and a second column for the 20-year-old observations (“Past”). Assume that the two samples are drawn from independent, normally distributed populations that have different standard deviations. Use this data set and the results from Question 1 to calculate the p-value for the hypothesis test. (Round your answer to three decimal places; add trailing zeros as needed.)
The p-value = type your answer…

3. Using the result from Question 2, identify the appropriate decision for the hypothesis test in Question 1, along with its interpretation. Use a = 0.01.
Reject Ho. There is sufficient evidence to support the original claim that the mean time between eruptions has decreased over the past 20 years.
Fail to reject There is sufficient evidence to support the original claim that the mean time between eruptions has decreased over the past 20 years.
Reject Ho. There is insufficient evidence to support the original claim that the mean time between eruptions has decreased over the past 20 years.
Fail to reject Ho- There is insufficient evidence to support the original claim that the mean time between eruptions has decreased over the past 20 years.
4. Suppose a scientist wants to test the claim that men and women have the same average BMI. To do so, they select independent samples of both men and women and measure their BMI. The sample statistics from the study are given in the following table:
BMI Study Sample Statistics
Male BMI Female BMI
Population mean Mi M2
Sample size 44 44
Sample mean 27.055 24.085
Sample standard deviation 7.808 4.029
Assume that BMI measurements are approximately normally distributed and that the measurements for men have a different standard deviation from that of women. Calculate a 95% confidence interval estimate for the mean difference between the average BMI measurement for men and women. (Round each of your answers to three decimal places; add trailing zeros as needed.)
The 95% confidence interval estimate is type your answer…