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Let p be the (unknown) proportion of males in a town of 100, 000 residents. A...

Let p be the (unknown) proportion of males in a town of 100, 000 residents. A political scientist takes a simple random sample of 100 residents from this town.

(a) Write down the exact pmf, as well as an approximate pmf, for the number of males in the sample. (They should both depend on p).

(b) If the number of males in the sample is 55 or more, the political scientist will claim that there are more males than females in the town. If the number of males in the sample is less than 55, he/she will claim that the number of males in the town is smaller or equal to that of females. What is approximately the probability that his/her claim will be correct if the true proportion of males in the town, p, is 50%? What if p = 55%?

(c) Report an approximate 68% confidence interval for p if 65 of the 100 residents in the sample are male.

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milcah answered 1 year ago
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