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  3. let p be the (unknown) proportion of males in a to

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

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Basic Math

Let p be the (unknown) proportion of males in a town of 100, 000residents. A political scientist takes a simple random sample of100 residents from this town.

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

(b) If the number of males in the sample is 55 or more, thepolitical scientist will claim that there are more males thanfemales in the town. If the number of males in the sample is lessthan 55, he/she will claim that the number of males in the town issmaller or equal to that of females. What is approximately theprobability that his/her claim will be correct if the trueproportion of males in the town, p, is 50%? What if p = 55%?

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

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