Problem
A publisher reports that $50 \%$ of their readers own a laptop. A marketing executive wants to test the claim that the percentage is actually different from the reported percentage. A random sample of 260 found that $42 \%$ of the readers owned a laptop. Find the value of the test statistic. Round your answer to two decimal places. Answer How to enter your answer (opens in new window) Tables Keypad Keyboard Shortcuts
Solution
Step 1 ：Given values are the sample proportion \(p_{hat} = 0.42\), the hypothesized population proportion \(p_0 = 0.50\), and the sample size \(n = 260\).
Step 2 ：We calculate the test statistic using the formula \(Z = \frac{{p_{hat} - p_0}}{{\sqrt{{p_0 * (1 - p_0) / n}}}}\).
Step 3 ：Substituting the given values into the formula, we get \(Z = \frac{{0.42 - 0.50}}{{\sqrt{{0.50 * (1 - 0.50) / 260}}}}\).
Step 4 ：Solving the above expression, we get \(Z = -2.5799224794555364\).
Step 5 ：Rounding the value of the test statistic to two decimal places, we get \(\boxed{-2.58}\).
