QuestionJuly 26, 2026

Claim: Fewer than 94% of adults have a cell phone. In a reputable poll of 1197 adults. 86% said that they have a cell phone. Find the value of the test statistic. The value of the test statistic is square (Round to two decimal places as needed.)

Claim: Fewer than 94% of adults have a cell phone. In a reputable poll of 1197 adults. 86% said that they have a cell phone. Find the value of the test statistic. The value of the test statistic is square (Round to two decimal places as needed.)
Claim: Fewer than 94%  of adults have a cell phone. In a reputable poll of 1197 adults. 86% 
said that they have a cell phone. Find the value of the test statistic.
The value of the test statistic is square 
(Round to two decimal places as needed.)

Solution
4.3(230 votes)

Answer

-11.65 Explanation 1. Identify parameters Null hypothesis p_0 = 0.94, sample proportion \hat{p} = 0.86, sample size n = 1197. 2. Calculate the test statistic Use the formula for the z-test of a proportion: z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1 - p_0)}{n}}} Substitute values: z = \frac{0.86 - 0.94}{\sqrt{\frac{0.94(1 - 0.94)}{1197}}} = \frac{-0.08}{\sqrt{\frac{0.0564}{1197}}} \approx \frac{-0.08}{0.006865} \approx -11.653

Explanation

1. Identify parameters<br /> Null hypothesis $p_0 = 0.94$, sample proportion $\hat{p} = 0.86$, sample size $n = 1197$.<br />2. Calculate the test statistic<br /> Use the formula for the z-test of a proportion: $z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1 - p_0)}{n}}}$<br /> Substitute values: $z = \frac{0.86 - 0.94}{\sqrt{\frac{0.94(1 - 0.94)}{1197}}} = \frac{-0.08}{\sqrt{\frac{0.0564}{1197}}} \approx \frac{-0.08}{0.006865} \approx -11.653$
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