7. A useful measure of the effectiveness of emergency response is the length of time from when a person calls 911 (the emergency phone number in the U.S.) until they arrive at the hospital via ambulance. A local emergency response team claims that their average time from the 911 call to the hospital is 45 minutes. Researchers in the UNC School of Nursing wanted to test whether the 45 minutes claim is correct. For a sample of 199 patients, researchers computed the time (number of minutes) from the 911 call to arrival at the hospital, finding a sample mean of 48.0 minutes. You may assume sigma=12.

a. Write the hypotheses (in symbols) for a two-sided test of theirclaim.

_________________________________________________________________________________

_______________b. Compute the test statistic for the hypotheses in (a).

_______________________c. If the null hypothesis is true, what is the distribution of the test statistic?

d. The p-value is 0.0004, or 0.04%. Interpret this p-value (i.e. there is a 0.04% chance that...).

_________________________________________________________________________________

_________________________________________________________________________________

e. Write the conclusion for your test based on your data, test statistic, and p-value. Make sure to include at least one sentence with no statistical terms/jargon.

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

f. A histogram of the data shows a slight positive skew and two outliers (Both outliers are 80 minutes, the next highest value is 68 minutes) do you have any concerns about the validity of the test? Why or why not?

_________________________________________________________________________________

_________________________________________________________________________________

_______________________g. Make a 95% confidence interval for the mean time from the 911 call to ambulance arrival at the ED.

h. What does the confidence interval in h. mean? In other words, interpret the confidence interval.

_________________________________________________________________________________

_________________________________________________________________________________