HonorsExam2

# HonorsExam2 - STA 2023 Honors Name Fall 2009 Exam 2 UF ID A...

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Unformatted text preview: STA 2023 Honors Name Fall 2009 Exam 2 UF ID# A 1- FORMULAS : Binomial Porportion p : mean = p stdev = M n — 0' Sample Mean X : mean = u stdev = T n 1. As part of a statistics class project, a group of students stationed themselves outside of Hume Hall on a Tuesday night. They asked 60 students entering and leaving the dorm how many text messages they had sent the previous day. The mean was 23.25 and the standard deviation 33.4. a) Let X be the number of text messages sent by each person. What can you say about the distribution of X? Explain. (5 pts) b) Let A7 be the average number of text messages for the sample. What can you say about the distribution of X ? Explain. (5 pts) 0) Construct a 95% conﬁdence interval for u. (8 pts) d) Interpret the conﬁdence interval, paying special attention to the assumptions, and the population the conclusions should be extended to. (5 pts) _____________J 2. Another group project wanted to estimate the proportion of “stoners” at UF. They asked the question: “In the past year, on average, did you smoke marijuana 3 or more times per month?” 52 out of 76 people answered yes. a) State the assumptions necessary for the validity of the conﬁdence interval. Are they satisﬁed? Explain. (5 pts) b) Construct a 96% conﬁdence interval for p and interpret. (12 pts) 3. If you wanted to estimate the proportion of “stoners” at UF to within 5% of the truth, with 95% conﬁdence, how large a sample should you take? (6 pts) 4. 5. A recent study considered whether daily consumption of 1200mg of garlic could reduce tick bites. The study used a crossover design with a sample of Swedish military conscripts, half of whom used placebo ﬁrst and garlic second, and half the reverse. Garlic was more effective for 37 of the subjects, and the placebo for 29 of them. Conduct the signiﬁcance test to determine if the study suggests a real beneﬁt to using garlic, or if the results consistent with random variation. Make sure you include all the steps, clearly marked, and your conclusions. (18 pts) True/False: 95% conﬁdence interval for the average amount of time students spend on Facebook each day: (1.3, 2.1). (10 pts) 95% of students spend between 1.3 and 2.1 hours on F acebook each day. Most students spend between 1.3 and 2.1 hours on F acebook each day. We are 100% conﬁdent that the average amount of time spent on F acebook each day by students in the sample is more than one hour. We are 95% conﬁdent that the average amount of time spent on Facebook each day by students in the population is more than one hour. Even if the sample is not truly random and representative of the population, the conﬁdence interval is still valid. 6. 7. 8. Experts determined that, because of the economy, 88% of American households were planning to cut back on their Halloween spending this year. We will select a random sample of 500 American households and ask them if they cutback this year. a) Let X be the number of people in the sample that answer “yes”. What is the distribution of X? Explain. (5 pts) b) Let f) be the proportion of people in the sample that answer “yes”. What is the distribution of f) ? Explain. (5 pts) c) Find the probability that more than 85% in the sample answer “yes”. (6 pts) Brieﬂy describe what the distribution of 1? would look like if we had: (3 pts) a) Normal population, n=5 b) Skewed right population, n=15 c) Uniform population, n=50 Brieﬂy explain when and why we use the t distribution. (2 pts) ...
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