Question

AP Stats Name Confidence Interval Activity Period tot reri Peanut Butter CANDY IN A CRUNCHY SHELL NET HT 439 You will work in a group of 4. Y confidence interval for the true proportion of orange Reeses our group will receive a cup of Reese's Pieces. Use this sample to calculate a 95% Pieces. Interpret your confidence interval. plems o re eses Left ρǐ be the prononton of gli orange

Answer 1

We have, n = 40, X = 21 p^n = X/n = 21/46 = 0.525 We have to 95% confidence interval for proportion & Formula is, p^n = E < p < p^n + E Where, E = Zc * squareroot p^n * (1 - p^n)/n Here, C = 0.95, alpha = 1 - C = 0.05 alpha_12 = 0.05/2 = 0.025 Add 0.95 & 0.025 = 0.975 This is area to the left side of ZC We can find Zc using excel type in excel, = NORMSRNV (0.975) ZC = 1.96 E = 1.96 times squareroot 0.525 * (1 - 0.525)/40 E = 0.1548 \r\n p^^- E = 0.525 - 0.1548 = 0.3702 p^^+ E = 0.525 + 0.1548 = 0.6798 The confidence interval is, 0.3702 < p < 0.6798 Conclusion: The true proportion of orange Reesels pieces is (0.3702, 0.6798)