3. At the Hawaii Pineapple Company, managers are interested in the size of the pineapples grown in the

company's fields. Last year, the mean weight of the pineapples harvested from one large field was 31

ounces with a standard deviation of 4 ounces. A different irrigation system was installed in this field

after the growing season. Managers wonder if the the mean weight of pineapples grown in the field this

year will be different from last.

(a) Write out the null Ho and alternative hypotheses Ha in terms of the population mean .

(b) If the managers choose to use a significance level of 0.05 and assume = 4 , identify their power to

detect a increase of 2 ounces in the mean (a = 33 ) if they look at a sample that is 30 pineapples

this year and use the two-sided alternative. Also identify the probability of making a type 2 error

with true a = 33 .

(c) Draw pictures of the null and alternative distributions of the means and shade the areas that

correspond to (i) Type 1 error, (ii) Type 2 error, and (iii) Power from part (b). (The online applet

from the notes may help.)

(d) Explain Type 1 and Type 2 errors of the test in context.

(e) What sample size should the managers use to ensure their test has power of at least 0.9 to detect

a = 33(assuming = 4 )?

(f) Explain why the managers may prefer to compute a 95%confidence interval instead of a two-sided

5%hypothesis test.