How Much Alcohol Do College Students Drink? According to the website www.collegedrinkingprevention.gov, "About 25 percen

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: How Much Alcohol Do College Students Drink According To The Website Www Collegedrinkingprevention Gov About 25 Percen 1 (80.69 KiB) Viewed 27 times

How Much Alcohol Do College Students Drink? According to the website www.collegedrinkingprevention.gov, "About 25 percent of college students report academic consequences of their drinking including missing class, falling behind, doing poorly on exams or papers, and receiving lower grades overall." A statistics student is curious about drinking habits of students at his college. He wants to estimate the mean number of alcoholic drinks consumed each week by students at his college. He plans to use a 90% confidence interval. He surveys a random sample of 71 students. The sample mean is 3.93 alcoholic drinks per week. The sample standard deviation is 3.78 drinks. Here is an applet you can use when directed to find the critical T-value. Note: the "Central Probability" is the area of the middle shaded region. T-distribution Inverse Calculator Central probability = 0.50 -4 -3 -2 0 2 3 t-score = 0.6750 central probability = 0.50 degrees of freedom = 50

1.25 / 1.25 pts Question 1 Have the conditions for constructing a confidence interval been met? No, there is no reason to believe that the number of alcoholic drinks consumed by students in the population is normally distributed. rect! Yes, the sample size is large enough. Correct. This sample size is large enough to insure the T-model is a good fit. No, the population standard deviation is unknown. 1.25 / 1.25 pts Question 2 Find the critical T-value for this 90% confidence interval. Hint: Use the applet to find the T-value for 90% confidence with df = 71 - 1 = 70. rect! 1.6669 t Answers 1.6669 (with margin: 0.001) Correct. The applets gives us a critical T-value of about 1.667.

1.25 / 1.25 pts Question 3 Find the margin of error for this 90% confidence interval. 0.75 Correct. The critical value for this 90% confidence interval is 1.667. So the margin of error is calculated as follows. 1.667 ( 3.78 0.75 71 0.89 0.78 1.25 / 1.25 pts Question 4 Find the 90% confidence interval. (3.48, 4.38) (3.18, 4.68) Correct. The confidence interval is calculated as follows. sample mean margin of error = 3.93 +0.75 (3.03, 4.53)

1.25 / 1.25 pts Question 5 Which of the following are an appropriate conclusion we can draw from this confidence interval? We are 90% confident that each student at this school consumed between 3.18 and 4.68 alcoholic drinks in the previous week. We expect 90% of all students on the campus to have consumed between 3.18 and 4.68 alcoholic drinks in the previous week. We are 90% confident that the mean number of alcoholic drinks consumed by all college students in the U.S. during the previous week is between 3.18 and 4.68. between 3.18 We are 90% confident that the mean number of alcoholic drinks consumed by all students at this college during the previous week and 4.68. Correct. A confidence interval gives us a range of values in which the population mean is likely to fall.

1.25 / 1.25 pts Question 6 Suppose the engineers want to make a 99% confidence interval. They plan to use the same sample of 45 cables. Use the applet to find the critical T-value they will use in the computation of the margin of error. 2.692 vers 2.6923 (with margin: 0.001) Correct. Setting df = 44 and Central Probability = 0.99 in the applet shows us that the critical T-value is about 2.692. Question 7 0/0.75 pts two decimal Construct the 99% confidence interval. Enter the lower bound of the interval (the smaller number). If necessary, round places. ed 774.26 vers 762.14 (with margin: 0.1) •Right one Incorrect. Based on a sample size of 45 cables, we found that the critical T-value for a 99% confidence interval is 2.692. We use this T-value to calculate our margin of error. Margin of error: T. = 2.692 . 15.1 45 Next we calculate the confidence interval. Confidence interval: TFT

0.5 / 0.5 pts Question 8 What is the upper bound of the 99% confidence interval? If necessary, round to two decimal places. 774.26 Jers 774.26 (with margin: 0.1) Correct. Based on a sample size of 45 cables, we found that the critical T-value for a 99% confidence interval is 2.692. We use this T- value to calculate our margin of error. Margin of error: T = 2.692. 15.1 Vn 45 6.06 Next we calculate the confidence interval. Confidence interval: TT.. & = 768.2 + 6.06 Vn The upper bound of the confidence interval is 768.2 + 6.06 = 774.26. 1.25 / 1.25 pts Question 9 In general, increasing the confidence level increases the margin of error. Answer 1: increases Correct. To be more confident that our confidence interval captures the population parameter, we need a larger margin of error. Increasing the confidence level makes the critical T-value bigger, which increases the margin of error.