Statistics - Solutions - Edubirdie

University:
California State University, Northridge
Course:
MATH 140 | Introductory Statistics
Academic year:

2012
Views:

339

Pages:

3
Author:

Haven Barry

Step 1: Name the Test and Check Conditions Test: Significance test for a single proportion Conditions: Randomness: Assume the spins were done at random Sample Size: np₀ = 40 * 0.5 = 20 > 10 n(1 - p₀) = 40 * (1 - 0.5) = 20 > 10 Population Size: 10n = 400 < total number of spins of pennies (infinitely many) Step 2: State the Hypotheses Null Hypothesis (H₀): P = P₀ Alternative Hypothesis (Hₐ): P ≠ P₀ Step 3: Calculate Test Statistic and z* z: (0.25 - 0.5) / √((0.5 * 0.5) / 40) = -3.162277 z:* ±1.96 (from the given significance level of 5%) Conclusion: Because z = -3.162277 < -1.96, the result is statistically significant. We reject the null hypothesis in favor of the alternative hypothesis. If the true proportion of heads was 50%, then it would be a rare event getting 10 out of 40 heads. So we have evidence to believe the standard of 50% is not true.

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