Question 7

Testing:
\[
\begin{array}{l}
H_{0}: p=0.92 \\
H_{1}: p \neq 0.92
\end{array}
\]

Your sample consists of 104 subjects, with 97 successes. Calculate the test statistic, rounded to 2 decimal places
\[
z=
\]
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Step 1 ：Calculate the sample proportion (p̂) using the formula: p̂ = number of successes / sample size. Substituting the given values, we get: p̂ = 97 / 104 = 0.9326923076923077

Step 2 ：Substitute the values into the formula for the z-score: z = (p̂ - p₀) / sqrt((p₀(1 - p₀)) / n). The given values are: p̂ = 0.9326923076923077, p₀ = 0.92, and n = 104

Step 3 ：Calculate the denominator of the z-score formula: sqrt((p₀ * (1 - p₀)) / n) = sqrt((0.92 * (1 - 0.92)) / 104) = 0.02830194339616981

Step 4 ：Substitute the calculated values into the z-score formula: z = (0.9326923076923077 - 0.92) / 0.02830194339616981 = 0.44871794871794873

Step 5 ：Round the calculated z-score to two decimal places: z = 0.45

Step 6 ：\(\boxed{0.45}\) is the final answer