Reference no: EM13995613
1. A national chain of health clubs says the mean amount of weight lost by members during the past month was at least 5 pounds. Skeptical of this claim, a consumer advocate believes the chain's assertion is an exaggeration. She interviews a random sample of 40 members, finding their mean weight loss to be 4.6 pounds, with a standard deviation of 1.5 pounds. At the 0.01 level of significance, evaluate the health club's contention.
2. In an interview with a local newspaper, a respected trial lawyer claims that he wins at least 75% of his court cases. Bert, a skeptical statistics student, sets up a one-tail test at the 0.05 level of significance to evaluate the attorney's claim. The student plans to examine a ran- dom sample of 40 cases tried by the attorney and deter- mine the proportion of these cases that were won. The null and alternative hypotheses are H0: 7T $ 0.75 and
H1: 7T , 0.75. Using the techniques of this chapter, Bert sets up a hypothesis test in which the decision rule is
"Reject H0 if z , 21.645, otherwise do not reject." What is the probability that Bert will make a Type II error (fail to reject a false null hypothesis) if the attor- ney's true population proportion of wins is actually
a. 7T 5 0.75?
b. 7T 5 0.70?
c. 7T 5 0.65?
d. 7T 5 0.60?
e. 7T 5 0.55?
f. Making use of the probabilities calculated in parts (a) through (e), describe and plot the power curve for Bert's hypothesis test.
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Determining the level of significance
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Constructing the power curve for the test
: Use the decision rule associated with part (a) and a range of selected assumed values for µ in constructing the power curve for the test.
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Mean amount of weight lost
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Draw the free body diagram of the blocks
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