Practice Problems for Test 3 1. (Chapter 4) A total of 120 people who have problems sleeping were selected and randomly divided into two groups. Group 1 is given an experimental drug, while Group 2 is given a placebo. After a week, the total number of hours of sleep per person that week in each group was recorded. a) Identify the experimental units. b) What is the response variable in this experiment? c) What is the explanatory variable? What are the levels of treatment? d) Is this a designed experiment or an observational study? e) Is this a matched pairs experiment? f) Is this a completely randomized experiment? g) If the researcher does not know who gets which pill, is this a double or single blind experiment? 2. (Chapter 4) A drug company has developed a new drug to relieve headache pain. The company randomly selects 100 adults that suffer from headaches. They ask these people to count how many headaches they have over a one month period. Then, these 100 adults are given the experimental drug. They are asked to take the drug once a day, and count how many headaches they have over a one month period. The company then takes the difference in the average number of headaches per person after taking the drug and the average number of headaches per person before taking the drug. a) Identify the experimental units. b) What is the response variable in this experiment? c) Is this a designed experiment or an observational study? d) Is this a matched pairs experiment? 3. (Chapter 4) Determine the type of sampling used. a) An interviewer in a mall is told to survey every fifth shopper, starting with the second. b) A researcher randomly selects 5 of the 70 hospitals in a metropolitan area and then surveys all of the surgical doctors in each of these 5 hospitals. c) A researcher segments the population of car owners into four groups: Ford, General Motors, Chrysler and foreign cars. She obtains a random sample from each group and conducts a survey. d) A list of students in elementary statistics is obtained in which the individuals are numbered 1 to 540. A professor randomly selects 30 of the students. 4) (8.1) The mean monthly expense for entertainment per household was obtained from data collected by telephone interviews of 1000 randomly selected households, and the 95% confidence interval was computed as: ($86.50, $161.50) a) Does the sample mean fall within the interval? If so, find its value. b) Does the population mean fall within the interval? If so, find its value. c) What is the margin of error? d) A magazine claims that on average households spend $120 per month on entertainment. Would we reject this claim? 5) (8.2) In a poll conducted in May 2000, a news agency took a simple random sample of 1068 Americans and asked them the following question ?Have you ever been on TV?? Of the 1068 Americans, 120 responded ?Yes? and the rest answered ?No.? a) Calculate the point estimate for the proportion of Americans that answered ?Yes? to this question. b) Can a valid 92% confidence interval be constructed for p? c) Determine the standard error and margin of error for a 92% confidence interval for p? d) Give the lower and upper limits for this 92% confidence interval. 6. (8.3) A random sample of 60 eggs from an egg farm was selected and each egg was weighed. The calculated sample mean was 2.1 oz. and the sample standard deviation was 0.35. A 90% confidence interval of the mean weight of eggs was constructed. a) If a 95% confidence interval was constructed using the same sample, which confidence interval would be wider: the 90% C.I. or the 95% C.I.? b) If a 90% confidence interval was constructed using a sample size of 100 eggs with the same sample mean of 2.1 oz, which 90% confidence interval would be narrower (this one or the n=60 one)? c) If you took 500 samples of 60 eggs and created a 90% confidence interval for each sample, approximately how many of these 90% confidence intervals would contain the population mean? 7. (8.3) In a random sample of n = 50 households, the average number of TV viewing hours per week was 35.3 with a sample standard deviation of 12.7 hours. Construct a 99% confidence interval for the mean number of TV viewing hours per week for the population. a) What is the point estimate? b) Find the standard error of the sample mean. c) To obtain a 99% confidence interval of the mean number of TV viewing hours per week in the population, what do we multiply the standard error by to find the margin of error? Find that value. d) For the 99% confidence interval, what is the margin of error? e) Find the upper and lower limits for the 99% confidence interval. 8. (8.4) In a previous sample taken in May 2000, 39% of the people polled answered ?yes? to the following question: ?do you happen to have in your home or garage any guns or revolvers?? How large a sample do we need to estimate the population proportion of ALL people who answered ?yes? to within 0.03 with a 95% level of confidence if? a) We want to use the May 2000 sample as our guideline? b) We don?t want to guess the proportion by using any previous study? c) Compare the results you obtained in a) and b). Is it something that you would expect? 9. (8.4) A doctor wants to estimate the mean serum HDL cholesterol of all 20-29 year old males. How many subjects would he need in order to estimate the mean serum HDL cholesterol of all 20-29 year old males to within 1.5 points with 95% confidence? Use a standard deviation of 12.5. Also, what would happen to the sample size if (i) we increase the margin of error, or (ii) the standard deviation increased? cricket3 Microsoft Word - Practice Problems for Test 3
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