Multiple Choice
Perform a 2-tailed hypothesis test for the true proportion of successes using the given values:
, , , & claim is
9. Hypothesis Testing for One Sample
Performing Hypothesis Tests: Proportions
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Perform a 2-tailed hypothesis test for the true proportion of successes using the given values:
, , , & claim is
A
Because -value = 0.465 > 0.01, we FAIL TO REJECT . There is NOT ENOUGH evidence to suggest : ≠ 0.75
B
Because -value = 0.465 > 0.01, we REJECT . There is ENOUGH evidence to suggest : ≠ 0.75
C
Because -value = 0.233 > 0.01, we REJECT . There is ENOUGH evidence to suggest : ≠ 0.75
D
Because -value = 0.233 > 0.01, we FAIL TO REJECT . There is NOT ENOUGH evidence to suggest : ≠ 0.75
Verified step by step guidance1
Step 1: Define the null hypothesis (H₀) and the alternative hypothesis (Hₐ). The null hypothesis is H₀: p = 0.75, and the alternative hypothesis is Hₐ: p ≠ 0.75, since this is a two-tailed test.
Step 2: Calculate the sample proportion (p̂). The formula for the sample proportion is p̂ = x / n, where x is the number of successes (28) and n is the sample size (40).
Step 3: Verify the conditions for using the normal approximation. Check if np ≥ 5 and nq ≥ 5, where q = 1 - p. Substitute the values of n, p, and q to ensure these conditions are met.
Step 4: Compute the test statistic (z). The formula for the z-value is z = (p̂ - p) / √[p(1 - p) / n]. Substitute the values of p̂, p, n, and q into the formula.
Step 5: Compare the calculated z-value to the critical z-value for α = 0.01 in a two-tailed test. Alternatively, calculate the p-value and compare it to α. If the p-value > α, fail to reject H₀; otherwise, reject H₀.
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