Question

Q: Would want to understand clearly and solve this example from Probability and Statistical Inference with the steps of the solution to better understand, thanks.

**Please give the step by step with details to completely see how the solution came about, plenty of thanks.

1) In a certain political campaign, one candidate has a poll taken at random among the voting population. The results are that y=150 out of n=360 voters favor this candidate.

(a) Construct a 98% confidence interval for the population.

(b) Using the data the candidate collected as the preliminary data, how large a sample must candidate select if she/he desires to be 98% confidence that the true proportion is within 0.02 of the sample proportion?

Answer 1

Solution:

Given: In a certain political campaign, one candidate has a poll taken at random among the voting population.

The results are that y=150 out of n=360 voters favor this candidate.

Then sample proportion is:

Part a) Construct a 98% confidence interval for the population proportion.

Formula:

where

Z_c is z critical value for c = 0.98 confidence level.

Find Area = ( 1+c)/2 = ( 1 + 0.98 ) / 2 = 1.98 /2 = 0.9900

Thus look in z table for Area = 0.9900 or its closest area and find corresponding z critical value.

Area 0.9901 is closest to 0.9900 , thus corresponding z value is 2.3 and 0.03

Thus Z_c = 2.33

Thus

Thus we get:

Thus a 98% confidence interval for the population proportion of voters who favor this candidate is between : ( 0.3562 , 0.4772).

Part b) Find sample size n:

Given: c = 98% confidence level

E = Margin of error = 0.02

p = 0.4167

Thus sample size is given by: