Question

Problem 3: A manufacturer of pens and pencils has created a new, ergonomically designed, mechanical pencil and plans to market it to college students. A random sample of 350 college students was selected and 287 said the new pencil felt more comfortable than other pencils. Calculate a 95% confidence interval for the proportion of college students who think the new pencil is more comfortable. (Don't use Minitab and show your work) a. Calculate a 95% confidence interval for the proportion of college students who think the new pencil is more comfortable. (Use Minitab, provide Minitab output and highlight confidence b. c. Interpret the interval above in terms of this problem.

Answer 1

a. Obtain the 95% confidence interval. Here, < < = 350,x = 287 Thus, P = 287/350 = 0.82 Thus, the 95% confidence interval is, CI = p plusminus squareroot p(1 - p)/n = 0.82 plusminus 1.960. squareroot 0.82(1 - 0.82)/350 = 0.82 plusminus 0.0402 = (0.7798,0.8602) Obtain the 95% confidence interval using MINITAB. MINITAB procedure: Stepl: Choose Stat > Basic Statistics > 1 Proportion. Step2: Choose Summarized data. Step3: In Number of events, enter 287. In Number of trials, enter 350. Step4: Click Options. Under Alternative, and choose not equal. Step5: Click OK in each dialog box. MINITAB output: Test and Cl for One Proportion Sample X N Sample p 95% Cl 1 287 350 0.820000 (0.779751, 0.860249) Using the normal approximation. From the MINITAB output, the 95% confidence interval is, Cl = (0.7798,0.8602) Conclusion: With 95% confidence it can be estimated that the proportion of college student found that the new pencil is more comfortable will lie between 0.7798, and 0.8602.