MATH 225N WEEK 6 QUIZ STATISTICS – QUESTION AND ANSWERS

MATH 225N WEEK 6 QUIZ STATISTICS – QUESTION AND ANSWERS Question 1 A statistics professor recently graded final exams for students in her introductory statistics course. In a review of her grading, she found the mean score out of 100 points was a x¯=77, with a margin of error of 10. Construct a confidence interval for the mean score (out of 100 points) on the final exam. ________________________________________ That is correct! ________________________________________ $$(67, 87) Answer Explanation Correct answers: • $left(67, 87right)$(67, 87) A confidence interval is an interval of values, centered on a point estimate, of the form (pointestimate−marginof error,pointestimate+marginof error) Using the given point estimate for the mean, x¯=77 and margin of error 10, the confidence interval is: (77−10,77+10)(67,87) FEEDBACK • • • • Content attribution- Opens a dialog Question 2 A random sample of adults were asked whether they prefer reading an e-book over a printed book. The survey resulted in a sample proportion of p′=0.14, with a sampling standard deviation of σp′=0.02, who preferred reading an e-book. Use the empirical rule to construct a 95% confidence interval for the true proportion of adults who prefer e-books. ________________________________________ That is correct! ________________________________________ $$(0.1, 0.18) Answer Explanation Correct answers: • $left(0.10, 0.18right)$(0.10, 0.18) By the Empirical Rule, a 95% confidence interval corresponds to a z-score of z=2. Substituting the given values p′=0.14and σp′=0.02, a confidence interval is (p′−z⋅σp′,p′+z⋅σp′)(0.14−2⋅0.02,0.14+2⋅0.02)(0.14−0.04,0.14+0.04)(0.10,0.18) FEEDBACK • • • • Content attribution- Opens a dialog Question 3 The pages per book in a library are normally distributed with an unknown population mean. A random sample of books is taken and results in a 95% confidence interval of (237,293) pages. What is the correct interpretation of the 95% confidence interval? ________________________________________ That is correct! ________________________________________ We estimate with 95% confidence that the sample mean is between 237 and 293 pages. We estimate that 95% of the time a book is selected, there will be between 237 and 293 pages. We estimate with 95% confidence that the true population mean is between 237 and 293 pages. Answer Explanation Correct answer: We estimate with 95% confidence that the true population mean is between 237 and 293 pages. Once a confidence interval is calculated, the interpretation should clearly state the confidence level (CL), explain what population parameter is being estimated, and state the confidence interval. We estimate with 95% confidence that the true population mean is between 237 and 293 pages. FEEDBACK • • • • Content attribution- Opens a dialog Question 4 The population standard deviation for the heights of dogs, in inches, in a city is 3.7 inches. If we want to be 95% confident that the sample mean is within 2 inches of the true population mean, what is the minimum sample size that can be taken? z0.101.282z0.051.645z0.0251.960z0.012.326z0.0052.576 Use the table above for the z-score, and be sure to round up to the nearest integer. ________________________________________ That is correct! ________________________________________ $$14 dog heights Answer Explanation Correct answers: