.A particular species of broad-tailed hummingbird is commonly found throughout the western United States. It is known that the mean incubation time for eggs of this bird follows a normal distribution with mean 16.5 days. However, at higher elevations (above 8000 feet), it is thought that the incubation period might be longer than 16.5 days. A number of broad-tailed hummingbird nests were located in mountain country above 8000 feet, and incubation times (in days) for 20 eggs are as follows.

15 19 16 16 18 17 14 18 15 15
17 16 17 19 16 15 18 20 18 17

We want to determine if the data indicate that the population mean incubation time above 8000 feet is greater
than 16.5 days. Use significance level 0.05.

(a) What are the null and alternative hypotheses?

A. H0:   16.5 vs. Ha:  > 16.5
B. H0:  = 16.5 vs. Ha:   16.5
C. H0:  > 16.8 vs. Ha:   16.8
D. H0:  = 16.8 vs. Ha:   16.8

(b) Identify the reference distribution

A. t, with degrees of freedom 19
B. t, with degrees of freedom 20
C. Normal
D. Approximately normal

(c) What is the value of the test statistic?
(d) Calculate the p-value for this test.
(e) Do we reject the null hypothesis?
(f) Do we conclude the mean incubation time above 8000 feet is greater than 16.5 days?