RVCC Statistics I Homework 4. Increasing confidence level results in: (choose all that apply) a) Margin of error increase b) Margin of error decrease c) Narrower confidence interval d) Wider confidence interval e) More precise estimate f) Less precise estimate 5. What is the meaning of a 95% confidence interval for one population mean? a) There is 95% probability that the population mean will be inside of the constructed confidence interval. b) If we construct 100 confidence intervals, 95 of them will cover the population mean. 6. The following data represent the levels of sulfate residuals obtained from photosynthesis of carbon-based substrate, measured in grams. A random sample of 15 substrates, taken from Fiji Islands, yielded the following amounts of residuals: 800, 633, 943, 847, 934, 841, 999, 1021, 342, 540, 550, 872, 809, 990, 1050 From previous studies, it is known that the population has approximately normal distribution. Construct and interpret 95% confidence interval for the mean sulfate residuals of all substrates on Fiji Islands. 7. The creator of the t-test, Gosset (who worked under the pseudonym Student) studied the effects of laevohysocyamine hydrobromide (LH) on sleep. The question was, does the chemical provide additional hours of sleep? He studied a random sample of 10 people using LH and these are the additional hours of sleep and found the average additional hours of sleep to be 2.33 hours, with a standard deviation of 2.00 hours . Construct and interpret a 95% confidence interval for the average additional sleep that would be obtained for the population of all people using LH. 8. A concerned professor wants to find out the average number of hours his students sleep. He asks his 15 students to tell him how many hours a night they sleep, and here are the results: 8, 10, 4, 6, 8, 3, 8, 6, 10, 3, 5, 5, 7, 8, 4 Consider the above data as a random sample of the professor's classes, construct and interpret a 90% confidence interval for the average number of hours of sleep. (Assume all assumptions are satisfied.)