Question

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 1 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 Hain terms of the population mean µ.

(b) If the managers choose to use a significance level of 0.05 and assume population standard deviation = 4, identify their power to detect an mean increase of 2 ounces µa = 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 µa = 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, (iii) Power. (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 ensuree their test has power of at least 0.9 to detect a mean increase of 2 ounces (assuming ? = 4)?

(f) Explain why the managers may prefer to compute a 95% confidence interval instead of a two-sided 5% hypothesis test.

Answer 1