(a) A test preparation company wants evidence that their course improves students' scores on the ACT...

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(a) A test preparation company wants evidence that their course improves students' scores on the ACT exam. From a random sample of 40 students who took the course, they do a paired t- test to compare the students' scores on the ACT exam before the course with their scores after the course (subtracting in the order (after - before)). The test has a test statistic of t = 2.06; what is the P-value of the test? Round to 3 decimal places. P = 0.045 (b) A researcher is interested in the effects of screentime on sleep. She wants to estimate the average number of hours of screentime that college students get between 9 pm and when they go to sleep. A random sample of 28 college students has an average amount of screentime after 9 pm of 1.4 hours with a standard deviation of 0.8 hours. Calculate a 95% confidence interval for the average amount of screentime that college students get between 9 pm and when they go to sleep. Round to 3 decimal places. CI = ( ) (c) A company that manufactures X-ray machines wishes to estimate the proportion of their machines that malfunction and produce excess radiation. A random sample of 56 of the machines is taken and 11 of the machines malfunction. Find a 90% confidence interval for the true proportion of the company's machines that malfunction. Round to 3 decimal places. CI = ( ) (a) A test preparation company wants evidence that their course improves students' scores on the ACT exam. From a random sample of 40 students who took the course, they do a paired t- test to compare the students' scores on the ACT exam before the course with their scores after the course (subtracting in the order (after - before)). The test has a test statistic of t = 2.06; what is the P-value of the test? Round to 3 decimal places. P = 0.045 (b) A researcher is interested in the effects of screentime on sleep. She wants to estimate the average number of hours of screentime that college students get between 9 pm and when they go to sleep. A random sample of 28 college students has an average amount of screentime after 9 pm of 1.4 hours with a standard deviation of 0.8 hours. Calculate a 95% confidence interval for the average amount of screentime that college students get between 9 pm and when they go to sleep. Round to 3 decimal places. CI = ( ) (c) A company that manufactures X-ray machines wishes to estimate the proportion of their machines that malfunction and produce excess radiation. A random sample of 56 of the machines is taken and 11 of the machines malfunction. Find a 90% confidence interval for the true proportion of the company's machines that malfunction. Round to 3 decimal places. CI = ( )