Problem

Claim: Fewer than $93 \%$ of adults have a cell phone. In a reputable poll of 1063 adults, $83 \%$ said that they have a cell phone. Find the value of the test statistic. The value of the test statistic is (Round to two decimal places as needed.)

Solution

Step 1 :We are given that the sample proportion (\(\hat{p}\)) is 0.83, the hypothesized population proportion (\(p_0\)) is 0.93, and the sample size (\(n\)) is 1063.

Step 2 :We can use these values to calculate the test statistic using the formula: \[Z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}\]

Step 3 :Substituting the given values into the formula, we get: \[Z = \frac{0.83 - 0.93}{\sqrt{\frac{0.93(1-0.93)}{1063}}}\]

Step 4 :Solving the above expression, we find that the value of the test statistic (\(Z\)) is approximately -12.78.

Step 5 :Final Answer: The value of the test statistic is \(\boxed{-12.78}\)

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Source: https://solvelyapp.com/problems/18581/

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