628 of 894 randomly selected adult Ghanaians aged 18 or older stated that a cand

Question

628 of 894 randomly selected adult Ghanaians aged 18 or older stated that a candidate's positions on the issue of family values are extremely or very important in determining their vote of president. a. Obtain a point estimate for the proportion of adult Ghanaians aged 18 or older who believe family values are extremely or very important in determining their vote for president. b. Verify the requirements for constructing a confidence interval for p are satisfied. c. Construct and interpret a 95% confidence interval for the proportion of adult Ghanaians aged 18 or older who believe family values are extremely or very important in determining their vote for president. d. Interpret the interval.

Explanation / Answer

proportion p = 628/894 = 314/447

a)

point estimate of proportion = 314/447 = 0.703

b)

np = 894 * 314/447 = 628

n(1-p) = 894 * 133/447 = 266

since np and n(1-p) are larger it satisfies the requirements

c)

standard error = sqrt(314/447 * 133/447 * 1/894)

= 0.01529

margin of error = z-score * standard error

= 1.96 * 0.01529

= 0.03

lower bound = 0.703 - 0.03 = 0.673

upper bound = 0.703 + 0.03 = 0.733

d)

proportion of adult aged 18 0r older who believe family values are important in determining their vote for president is between 0.673 and 0.733

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