## Elementary Statistics: A Step-by-Step Approach with Formula Card 9th Edition

Given $p=0.205, n=120, \hat p=38/120=0.317$ a. State the hypotheses and identify the claim. $H_o: p\leq 0.205$ $H_a: p\gt 0.205$ (claim, right tail test) b. Find the critical value(s). $\alpha=0.10, z_c=1.28, E=1.28\times\sqrt {\frac{0.317\times0.683}{120}}=0.054$ c. Compute the test value. $z=\frac{0.317-0.205}{\sqrt {0.205\times0.795/120}}=3.04$ The confidence interval is $(0.317-0.054, 0.317+0.054)$ which gives $0.263\leq p\leq 0.371$ d. Make the decision. Confidence interval test: the range of predicted proportion is larger than 0.205 which confirms the claim. Hypothesis test: $z\gt z_c$ we have enough evidence to reject the null hypothesis and support the claim. e. Summarize the results. We used both confidence interval and hypothesis tests and conclude that at $\alpha=0.1$, the proportion is greater than $20.5\%$