M 140 Test 2 A Name__________________ SHOW YOUR WORK FOR FULL CREDIT! Problem Max. Points Your Points 1-10 10 11 5 12 4 13 12 14 6 15 17 16 6 17 Extra Credit 4 Total 60 1 Multiple Choice Questions (1 point each) 1. A new headache remedy was given to a group of 25 subjects who had headaches. Four hours after taking the new remedy, 20 of the subjects reported that their headaches had disappeared. From this information you conclude: a. that the remedy is effective for the treatment of headaches. b. nothing, because the sample size is too small. c. nothing, because there is no control group for comparison. d. that the new treatment is better than aspirin. e. that the remedy is not effective for the treatment of headaches. 2. In the Faculty of Science of a university there are ten departments. Two faculty members are selected at random from each department. The sample of twenty faculty members selected in this way is called a: a. Simple random sample. b. Systematic sample. c. Stratified random sample. d. Voluntary response sample. e. Multistage sample. 3. A simple random sample of 1200 adult Americans is selected and each person is asked the following question. "In light of the huge national deficit, should the government at this time spend additional money to establish a national system of health insurance?" Only 39% of those responding answered yes. This survey a. is reasonably accurate since it used a large, simple random sample. b. probably overstates the percentage of people that favor a system of national health insurance. c. probably understates the percentage of people that favor a system of national health insurance. d. is very inaccurate, but neither understates nor overstates the percentage of people that favor a system of national health insurance. Since simple random sampling was used, it is unbiased. Use the following to answer questions 4–5: A marketing research firm wishes to determine if the adult men in Laramie, Wyoming, would be interested in a new upscale men’s clothing store. From a list of all residential addresses in Laramie, the firm selects a simple random sample of 100 and mails a brief questionnaire to each. 4. What is the population of interest? a. All adult men in Laramie, Wyoming. b. All residential addresses in Laramie, Wyoming. c. The members of the marketing firm that actually conducted the survey. d. The 100 addresses to which the survey was mailed. 5. One particular neighborhood in Laramie happens to have exactly 100 residential addresses. What do we know about the chance that all 100 homes in that neighborhood end up being the sample that is selected? a. It is the same as for any other set of 100 residential addresses. b. It is exactly 0. Simple random samples will spread out the addresses selected. c. It is reasonably large due to the “cluster” effect. d. It is 100 divided by the size of the population of Laramie. e. It is much less likely than most sets of 100 residential addresses from Laramie are. 2 6. There are two statistics classes. The first has 350 students and the second has 250 students. In the first class the students are instructed to each toss a coin 20 times and record the value of p$ , the proportion of heads. The instructor them makes a histogram of the 350 values of p$ obtained. The second class did the same, except that each student tossed a coin 40 times. The histogram of p$ values for the first class should be a) more biased since it is based on a smaller number of tosses. b) more variable since it is based on a smaller number of tosses. c) less variable since it is based on a larger number of students. 7. A large university wishes to determine the percentage of its students that have committed some form of academic dishonesty, such as cheating on an examination or plagiarism on assignments during their academic career. To estimate this percentage, a random sample of their current students is selected. Each selected student is then interviewed by a staff member and asked if they had cheated. The results of this survey likely will be unreliable because a. some students likely will refuse to answer the question. b. those students who answer the question may not do so honestly. c. the interviewer being a staff member may be intimidating and hence there may be response bias. d. All of the above are reasons for concern. 8. A telemarketing firm in Los Angeles uses a device that dials residential telephone numbers in the city at random. Of the first 100 numbers dialed, 48% are unlisted. This is not surprising because 52% of all Los Angeles residential phones are unlisted. a. the 52% is a parameter, and the 48% is a statistic b. the 52% is a statistic, and the 52% is a parameter c. both the 52% and the 48% are parameters d. both the 52% and the 48% are statistics 9. A polling agency took a random sample of 1000 likely voters in Florida (population: about 18 million), and another random sample of 1000 likely voters in New Mexico (population: about 2 million). a. the sampling variability of the Florida poll will be greater than that of the New Mexico poll b. the sampling variability of the Florida poll will be less than that of the New Mexico poll c. the sampling variability of the Florida poll will be about the same as for the New Mexico poll 10. Which one of the following statements is false? a. An appropriate statistical notation for the fraction of all American adults who received at least one speeding ticket last year is p. b. We cannot predict the likely accuracy of an estimate obtained from a sample if the sample is not taken randomly. c. Usually a parameter value will fall within the interval specified by the point estimate plus and minus its margin of error, but this is not guaranteed to happen. d. When the z-score of a data value is 1.8, that means that the data value could be 1.8 standard deviations either above or below the mean. 3 11. (5 points) Fill in the blanks. To make it easier for you, here’s the list of possible terms to use: Sampling variability Sampling design Sampling distribution Sampling error Sampling frame A list of potential individuals or objects to be sampled is called ___ sampling frame _______ . Simple random sampling, stratified random sampling, and multistage random sampling are the most common types of ____ sampling design _____ . The fact that different random samples from a population will give somewhat different results is called _____ sampling variability ______. The distribution of the sample statistic for all the possible SRSs of the same size from the same population is called the ____ sampling distribution ______ . The fact that even well constructed samples will give results that are somewhat different from the population value simply because the entire population is not sampled is called ___ sampling error ___ . 12. The drawings represent various sampling methods. Match the pictures with the sampling methods. A. Stratified Random Sampling B. Systematic Sampling C. Simple Random Sampling D. Cluster Sampling 13. An Australian study included 588 men and women who already had some pre-cancerous skin lesions. Half got a skin cream containing a sunscreen with a sun protection factor of 17; half got an inactive cream. After 7 months, those using the sunscreen with the sun protection had fewer new pre-cancerous skin lesions (New England Journal of Medicine) . a. What are the explanatory and response variables? Explanatory variable: the two types of skin creams Response variable: the number of pre-cancerous skin lesions 4 b. Explain what the placebo was in this study, and why they included it. The placebo is the inactive skin cream. The control group received the placebo. This provides the basis for comparison. Without a placebo group to compare against, it is not possible to know whether the treatment itself had any effect. c. This experiment was also a double-blind study. Explain what that means and why they used that. Double-blind experiment means that neither the subjects nor the experimenter knows which group gets the treatment (the skin cream with the sunscreen) and the placebo (the inactive cream). This eliminates observer or experimenter bias, as experimenters may unwittingly bias participants because they expect them to respond in a particular way. d. Draw the outline of the study. Make sure you indicate the response variable, and group sizes. Treatment group: 294 subjects 588 randomly Skin cream with selected subjects sunscreen Compare number of pre- with some pre- Random cancerous skin lesions after cancerous skin assignment 7 months lesions Control group: 294 subjects Placebo e. The experimenters suspected that gender could be one of the lurking variables. Explain briefly what they could do to control for this variable. They could do a block design separating the subjects by gender, and doing the experiment with both genders. f. Explain where at what point in the study the experimenters should use random assignment : When they separate the subjects into the two groups. They should randomly decide which subject goes to which group. 5 14. The effect of alcohol consumption on the body appears to be much greater at high altitudes than at sea level. To test this theory, a scientist randomly selected 40 subjects and used a design in which each person acted as his or her own control.