Problem

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 \[ z= \] Submit Question

Solution

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

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Source: https://solvelyapp.com/problems/GTEPIHlY3w/

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