Question

We wish to gather some information relating to the average time a hospitalized Eagle Flu patient remains in the hospital. We randomly sample 16 cured formerly hospitalized Eagle Flu patients and these were the number of days spent in the hospital:

6.09, 8.04, 6.43, 8.58, 10.34, 5.40, 9.87, 9.24, 9.18, 5.06, 5.39, 5.89, 11.91, 8.94, 5.68, 9.85


Many surveys of flu hospital stays show that hospitalization length is normally distributed. So, we assume that our sample comes from a normal population with unknown mean of μ days and an unknown standard deviation of σ days. We would like to test whether the average hospital stay length is less than 8.1 days..
The null hypothesis is thus

H₀:μ=8.1

. We will test this against the alternative

H_a

.

We want to test at the 8% level.

Let x = the sample mean and s = the sample standard deviation.



f) Calculate the critical value, tstar, for your test.(negative value)
g) For what values of your test statistic, T, is the null hypothesis rejected?

T > tstar or T < -tstar T > tstar/2 or T < -tstar/2     T > tstar |T - tstar| < .09 T < tstar

h) Calculate the p-value for this test.
i) Is the null hypothesis rejected? (Y/N)

N Y    

j) If we ran 800 8% level tests then about how many times would we make a Type I error?

k) Create a 92% confidence interval for μ using this data.

Answer 1

j) Number of times one would make a Type I error = 800*0.08 = 64

k)