Question

A magazine provided results from a poll of 1000 adults who were asked to identify their favorite pie. Among the

1000 respondents,11% chose chocolate pie, and the margin of error was given as plus or minus±5 percentage points. Given specific sample data, which confidence interval is wider: the 90% confidence interval or the 80% confidence interval? Why is it wider?

Choose the correct answer below.

A. A 90% confidence interval must be wider than an 80% confidence interval in order to be more confident that it captures the true value of the population proportion.

B. An 80% confidence interval must be wider than a 90%confidence interval because it contains100%minus−8080%equals=20% of the true population parameters, while the 90% confidence interval only contains 100%minus−9090%equals=1010% of the true population parameters.

C.An 80% confidence interval must be wider than a 90% confidence interval in order to be more confident that it captures the true value of the population proportion.

D. A 90% confidence interval must be wider than an 80%confidence interval because it contains 90% of the true population parameters, while the 80%confidence interval only contains 80%of the true population parameters.

Answer #1

Solution

**Option A Answer 1**

**Explanation**

Theoretically, 100(1 - α) % Confidence Interval for the population proportion, p is:

p_{hat} ± MoE, where MoE =
Z_{α/2}[√{p_{hat} (1 – p_{hat})/n}]

with

Z_{α/2} is the upper (α/2)% point of N(0, 1),

p_{hat} = sample proportion, and

n = sample size.

The width of the confidence interval depends only on MoE which
in turn depends on Z_{α/2} only when other things remain
the same.

As confidence level increases, α decreases and as α decreases,
Z_{α/2} increases resulting in wider interval.

Physically, more confidence can be gained only by widening the interval.

**DONE**

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