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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.
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