A scientific paper reported the following summary information on fracture toughnesses (MPa) of n = 169 ceramic bars fired in a particular kiln: = 89.10, s = 3.73. a) Calculate a confidence interval (bilateral) for the average true fracture toughness using a 95% confidence level. Could it be said that the average true fracture toughness was accurately estimated? b) Assume that the investigators believed a priori that the population standard deviation was approximately 4 MPa. Based on this assumption, how large a sample would have to be to estimate μ to within 0.5 MPa with 95% confidence for each side? Note: The exercise in the image is in Spanish, to make the exercise more understandable.

psda q1

In a random sample of 27 people, the mean commute time to work was 31.3 minutes and the standard deviation was 7.3 minutes. Assume the population is normally distributed and use a t-distribution to construct a 90% confidence interval for the population mean u. What is the margin of error of µ? Interpret the results. The confidence interval for the population mean is (OD. (Round to one decimal place as needed.) The margin of error of u is (Round to one decimal place as needed.) Interpret the results. O A. It can be said that 90% of people have a commute time between the bounds of the confidence interval. B. With 90% confidence, it can be said that the population mean commute time is between the bounds of the confidence interval. C. With 90% confidence, it can be said that the commute time is between the bounds of the confidence interval. D. If a large sample of people are taken approximately 90% of them will have commute times between the bounds of the confidence interval.

Here are summary statistics for the weights of Pepsi in randomly selected​ cans: n=36​, x=0.82411 ​lb, s=0.00567 lb. Use a confidence level of 99​% to complete parts​ (a) through​ (d) below.       Question content area bottom Part 1 a. Identify the critical value tα/2 used for finding the margin of error.