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Chapter 10 p2

Allied Corporation is trying to determine whether to purchaseMachine A or B. It has leased the two machines for a month. Arandom sample of 5 employees has been taken. These employees havegone through a training session on both machines. Below you aregiven information on their productivity rate on both machines. (Letthe difference d = Machine A - Machine B.)

	Productivity Rate
Person	Machine A	Machine B
1	47	52
2	53	58
3	50	47
4	55	60
5	45	53

?

Assume the population of differences is normallydistributed.

a.	State the null and alternative hypotheses for a lower tailtest.
b.	Find the mean and standard deviation for the difference.
c.	Compute the test statistic.
d.	Test the null hypothesis, stated in Part a, at the 10%level.

ANSWER:

? a. H0: ?d ? 0 Ha: ?d < 0 b. -4 and 4.123 c. t = -2.169 d. p-value (.048) < .10, rejectH0

A poll was taken this year asking college students if theyconsidered themselves overweight. A similar poll was taken fiveyears ago. Results are summarized below. Has the proportionincreased significantly? Let ? =.05.

	Sample Size	Number Considered Themselves Overweight
Present Sample	300	150
Previous sample	275	121

ANSWER:

H0: p1 -p2 ? 0 Ha: p1 -p2 > 0 z = 1.44; p-value = .0749; do not rejectH0; there is no sufficient evidence to concludethat the proportion has increased significantly.