Statistics 2101 - Dr. Wilson
Spring 1996
Homework #9.

Chapter 10
==========

1. Suppose that you are interested in studies of heights of
American men, a variable known to be approximately normally
distributed in the population. Let us assume that the mean height
in the population of American men (mu) is equal to 68 inches and
the population standard deviation (sigma) is equal to 3.2 inches.
Suppose now that you randomly draw one sample of N=100 midwestern
American men, and you calculate the mean height of this sample as
xbar = 67.4 inches and the standard deviation of the sample as s =
3.5 inches. Using these data, decide whether the average height
of midwestern men is different from the average of the entire US
adult male population (Use a level of significance equal to .05).

a) State the Null and Alternative Hypotheses (using symbols).

b) Specify the decision criterion and draw the rejection region.

c) Compute the test statistic.

d) Make a decision about the null hypothesis. In addition, state
     your conclusion in english.



2. Suppose that the population standard deviation (sigma) is actually
2.2 inches, and we decide to use a level of significance of .01
(Everything else remains the same).  Redo problem # 1 using the
new data, following steps a through d.



3. Frito-Lay corporation claims that their bags of Doritos
tortilla chips contain 269.8 grams. To test their claim, I
weighed the contents of eight packages of Doritos tortillas
(Nacho cheese flavor) on a scale in my lab. The mean weight of
this sample of Doritos bags was xbar= 270.39 grams, with a standard
deviation of s = 0.52 gram. According to our data, is the claim
that Doritos bags weigh 269.8 grams justified? (Use a
significance level of .01).

a) State the Null and Alternative Hypotheses (using symbols).

b) Specify the decision criterion and draw the rejection region.

c) Compute the test statistic.

d) Make a decision about the null hypothesis. In addition, state
     your conclusion in english.



4. Suppose I ask you now the following question: Do Doritos bags
weigh MORE than 269.8 grams. Using the data from problem # 3
answer this ONE-tailed question. Again, follow steps a through d.



Chapter 11
==========

5. Imagine being lost at sea, bobbing around in an orange life
jacket. The Coast Guard sends out two kinds of observers to find
you: fellow humans and pigeons. Each observer is successful; the
search time in minutes for each observer is given in the table.
Analyze the results and write a conclusion about the performance
of the two types of observers.

	Humans	Pigeons

	45	31

	63	24

	39	20


a) Calculate the mean and standard deviation of each sample.

b) State the Null and Alternative Hypotheses.

c) What are the critical values of t? (Use alpha = .05)

d) Compute the test statistic.

e) Make a decision.