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1. What's wrong? Explain what is wrong with each of the following:
(a) An approximate 99% con?dence interval for an unknown proportion p is pˆ plus or minus its standard error.
(b) When performing a large-sample signi?cance test for a population proportion, the t distribution is used to compute the P-value.
(c) A signi?cance test is used to evaluate H0 : pˆ = 0.2 versus the two-sided alternative.
2. pˆ and the Normal distribution. Consider the binomial setting with n = 60 and p = 0.4.
(a) The sample proportion pˆ will have a distribution that is approximately Normal. Give the mean and the standard deviation of this Normal distribution.
(b) Draw a sketch of this Normal distribution. Mark the location of the mean.
(c) Find a value p∗ for which the probability is 95% that pˆ will be between ±p∗. Mark these two values on your sketch.
The Financial Advisor exam has a mean of 500 and a standard deviation of 20. If the bank chooses to hire either Steve or Mark based solely on their exam performance, who is the bank more likely to hire? Show evidence for your answer.
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