1. (a) Estimate the population proportion p where a random sample of 1000 is dra

Question

1. (a) Estimate the population proportion p where a random sample of 1000 is drawn with sample proportion .65. Find a 90% confidence interval and a 95% confidence interval Comment on the error in the estimate vis-a-vis the sample size. Answer the same question assuming a sample size of 2000.
Note: Please, show all the work/steps, to receive points. Thank you.

(b) A researcher believes that the proportion of a certain population is at most 50%; A random sample of l200 is selected and the sample proportion turns out to be 47%. Test the researcher’s claim at the 5% level of significance.
Note: Please, show all the work/steps, to receive points. Thank you.

(c) A candidate for office wishes to estimate the percent of the voting population favoring her candidacy. A random sample of 1300 is drawn from the population of potential voters and the percentage for the sample turns out to be 48%. Find a 95% confidence interval for the true proportion favoring her candidacy.
Note: Please, show all the work/steps, to receive points. Thank you.

Explanation / Answer

a. The estimate of the population proportion is the same as the sample proportion, .65. A 90% confidence interval is p +/- 1.645 * sqrt p(1-p)/n So here we have .65 +/- 1.645* sqrt .65*.35/1000= .65+/- .025= (.625, .675) A 95% would be .65 +/- 1.96 sqrt .65*.35/1000= .65 +/- .030= (.62, .68) For 2000 we would have: 90% .65 +/- 1.645 sqrt .65*.35/2000= .65+/- .018= (.632, .668) 95% .65+/- 1.96 sqrt .65*.35/2000= .65 +/- .021= (.629, .671) b) Ho: P> .5, Ha P

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