# Hypothesis testing

1) The FMA Company has designed a new type of 16 lb. bowling ball. The company knows that the average man who bowls in a scratch league with the company's old ball has a bowling average of 155. The variance of these averages is 100. The company asks a random sample of 100 men bowling in scratch leagues to bowl for five weeks with their new ball. The mean of bowling averages for these men with the new ball is 170. There is no reason to believe the variance is any different with the new ball. Test the null hypothesis that the new ball does not improve a bowler's average at the 5% level of significance.

2) A home owner claims that the current market value of his house is at least $40,000. Sixty real estate agents were asked independently to estimate the house's value. The hypothesis test that followed ended with a decision of "reject H(O)". Which of the following statements accurately states the conclusion?

a) The home owner is right, the house is worth $40,000.

b) The home owner is right, the house is worth less than $40,000.

c) The home owner is wrong, the house is worth less than $40,000.

d) The home owner is wrong, the house is worth more than $40,000.

e) The home owner is wrong, he should not sell his home.

3) A reading coordinator in a large public school system suspects that poor readers may test lower in the standardized math test than children whose reading is satisfactory. He draws a random sample of 30 fifth grade students who are poor readers. Historically fifth grade students in the school system have had an average score of 105 on the test. The sample of 30 has XBAR = 101.5 and Stand dev = 1.42. Test the appropriate hypothesis at the 5% level.

4) Suppose in a sample of 25 people, the mean height XBAR was observed to be 70 inches. Suppose also SIGMA = 3.

A. Would you reject the hypothesis H(0):MU = 71 versus H(1):MU =/= 71 on the basis of the observations, when testing at level ALPHA = .05?

B. Would you reject the hypothesis H(0):MU = 72 versus the alternative H(1):MU =/= 72 on the basis of the observations, when testing at level ALPHA = .05?

5) To test H(0): MU = 20 vs. H(A): MU =/= 20, a sample of 400 will be taken from a large population, whose standard deviation is 5. H(0) will be rejected if XBAR >= 20.5 or XBAR <= 19.5. The level of significance of this test is approximately:

6) In a sample of 25 physicians, the mean annual income of $47,000 with a variance of $360,000. Would the null hypothesis that the true mean is $50,000 be continued or rejected at the 5% significance level? Why?

7) Nine men with a genetic condition that causes obesity entered weight reduction program. After four months the statistics of weight loss were: XBAR = 11.2, S = 9.0. The researcher wants to test the hypothesis: The average four-month weight loss in such a program is <= 6 pounds verses the alternative: > 6 pounds at a 5% significance level. Given the data of our problem, what can we conclude?

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