Problem

Claim: Most adults would erase all of their personal information online if they could. A software firm survey of 539 randomly selected adults showed that $55 \%$ of them would erase all of their personal information online if they could. Find the value of the test statistic. The value of the test statistic is (Round to two decimal places as needed.)

Solution

Step 1 :The test statistic for a proportion is calculated using the formula: \(Z = \frac{{\hat{p} - p}}{{\sqrt{\frac{{p(1 - p)}}{n}}}}\) where \(\hat{p}\) is the sample proportion, p is the hypothesized population proportion, and n is the sample size.

Step 2 :In this case, the hypothesized population proportion (p) is not given. However, since the claim is that 'most' adults would erase their information, we can assume that p = 0.5 (i.e., 50%). The sample proportion (\(\hat{p}\)) is 0.55 (or 55%) and the sample size (n) is 539.

Step 3 :Let's plug these values into the formula and calculate the test statistic.

Step 4 :\(\hat{p} = 0.55\)

Step 5 :p = 0.5

Step 6 :n = 539

Step 7 :Z = \(\frac{{0.55 - 0.5}}{{\sqrt{\frac{{0.5(1 - 0.5)}}{539}}}}\)

Step 8 :\(\boxed{Z \approx 2.32}\)

From Solvely APP
Source: https://solvelyapp.com/problems/22717/

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