QuestionJuly 15, 2025

Claim: Fewer than 95% of adults have a cell phone. In a reputable poll of 1089 adults, 87% 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 95% of adults have a cell phone. In a reputable poll of 1089 adults, 87% 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 95%  of adults have a cell phone. In a reputable poll of 1089 adults, 87%  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
4.2(188 votes)

Answer

The value of the test statistic is -10.12. Explanation 1. Identify the null and alternative hypotheses Null hypothesis H_0: p = 0.95; Alternative hypothesis H_a: p < 0.95. 2. Calculate the sample proportion Sample proportion \hat{p} = \frac{87}{100} = 0.87. 3. Compute the standard error Standard error SE = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.95 \times 0.05}{1089}}. 4. Calculate the test statistic Test statistic z = \frac{\hat{p} - p}{SE} = \frac{0.87 - 0.95}{\sqrt{\frac{0.95 \times 0.05}{1089}}}. 5. Simplify and round the result Calculate the value and round to two decimal places.

Explanation

1. Identify the null and alternative hypotheses<br /> Null hypothesis $H_0$: $p = 0.95$; Alternative hypothesis $H_a$: $p < 0.95$.<br /><br />2. Calculate the sample proportion<br /> Sample proportion $\hat{p} = \frac{87}{100} = 0.87$.<br /><br />3. Compute the standard error<br /> Standard error $SE = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.95 \times 0.05}{1089}}$.<br /><br />4. Calculate the test statistic<br /> Test statistic $z = \frac{\hat{p} - p}{SE} = \frac{0.87 - 0.95}{\sqrt{\frac{0.95 \times 0.05}{1089}}}$.<br /><br />5. Simplify and round the result<br /> Calculate the value and round to two decimal places.
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