Question

In: Statistics and Probability

A random sample of 283 adult Canadians was taken, and 205 of them said that they...

A random sample of 283 adult Canadians was taken, and 205 of them said that they always vote in federal general elections. Find a 92% confidence interval for the proportion of adult Canadians who say that they always vote in federal general elections

Expert Solution

Solution:

Given:

n = Number of adult Canadians selected in a random sample

n = 283

x = Number of adult Canadians said that they always vote in federal general elections

x = 205

Thus sample proportion of adult Canadians said that they always vote in federal general elections is:

We have to find a 92% confidence interval for the proportion of adult Canadians who say that they always vote in federal general elections.

Formula:

where

Z_c is z critical value for c = 0.92 confidence level.

Find Area = ( 1+c)/2 = ( 1 + 0.92 ) / 2 = 1.92 /2 = 0.9600

Thus look in z table for Area = 0.9600 or its closest area and find corresponding z critical value.

Area 0.9599 is closest to 0.9600 and it corresponds to 1.7 and 0.05

Thus Z_c = 1.75

Thus

( Round final answer to specified number of decimal places)

Thus we are 92% confident that the true value of population proportion of adult Canadians who say that they always vote in federal general elections is between the limits: ( 0.6779 , 0.7709).

orchestra answered 1 year ago

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