STAT1034 - Ch3 and Ch4 StudyTest

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Apr 3, 2024

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Item: Homework 3 Score: 28/28 100% (Calculated) scaled to 100/100 100% Class Statistics Due: Friday, May 27, 2016 11:59 PM Due (late): Saturday, May 28, 2016 12:14 AM Submitt ed: Thursday, May 26, 2016 5:43 PM Answer s: 1. Vitamin D is needed for the body to use calcium. An experiment is designed to see the effects of calcium and vitamin D supplements on the bones of first-year college students. The outcome measure is the total body mineral content (TBBMC), a measure of bone health. Three doses of calcium will be used: 0, 200, and 400 mg/day. The doses of vitamin D will be 0, 50, and 100 international units (IU) per day. The calcium and vitamin D will be given in a single tablet. All tablets including those with no calcium and no vitamin D will look identical. Subjects for the study will be 90 men and 90 women. Identify the correct factor(s) and the number of treatments for this experiment. The factors are calcium dose and vitamin D dose. There are nine treatments. The factors are calcium dose and vitamin D dose. There are six treatments. The factor is first-year college students. There are two treatments. The factor is total body mineral content (TBBMC). There are nine treatments. The factors are calcium dose, and vitamin D dose. There are nine treatments (each calcium/vitamin D combination). Score: 1 of 1 2. Step 1: Table B is a table of random digits. Which of the following statements are true of a table of random digits, and which are false? Explain your answers. True or False: There are exactly four 0s in each row of 40 digits. True

False Step 2: Table B is a table of random digits. Which of the following statements are true of a table of random digits, and which are false? Explain your answers. True or False: Each pair of digits has chance of being 00. True False Step 3: Table B is a table of random digits. Which of the following statements are true of a table of random digits, and which are false? Explain your answers. True or False: The digits 0000 can never appear as a group, because this pattern is not random. True False Score: 3 of 3 3. Consider the scenario: The population consists of all individuals selected in a simple random sample. Identify the correct statement about the given scenario. The scenario describes the population and sample clearly for a simple random sample. The scenario describes a census. The scenario describes a stratified sample. This given scenario confuses the ideas of population and sample. If the entire population is found in our sample, we have a census rather than a sample.

Score: 1 of 1 4. In using Table B repeatedly to choose samples or do randomization for experiments, you should not always begin at the same place, such as line 101. Why not? If we start regularly at the same line of Table B the results are not purely random. Correct Starting at line 101 is equivalent to starting at any other line of Table B, as far as randomization is concerned. Therefore, we are free to start at any line we want even if it is the same line regularly. Because line 101 is already determined, then using it regularly is totally not random. The chance of a specific digit to appear is reduced and therefore randomization is impaired. Score: 1 of 1 5. Step 1: See the given figure. The 44 blocks in this tract are divided into three “block groups.’’ Group 1 contains 6 blocks numbered 1000 to 1005; Group 2 (outlined in the given figure) contains 12 blocks numbered 2000 to 2011; Group 3 contains 26 blocks numbered 3000 to 3025. Choose a stratified sample of two blocks from the 6 blocks in Group 1, two from the 12 blocks in Group 2, and three from the 26 blocks in Group 3.

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The simplest method of selecting the stratified sample is: Starting at any line of Table B find the first two numbers between 0 and 5, followed by the next two different numbers between 00-11, and finally the next three different numbers between 00-25. Assign labels 01-44 to all blocks and select a sample of size 6. Assigning the labels 01-025 to each of the blocks in each group and then choosing the three samples from the three groups as required. Use the original labeling and choose the 3 samples from the 3 groups as required. Step 2:

See the given figure. The 44 blocks in this tract are divided into three “block groups.’’ Group 1 contains 6 blocks numbered 1000 to 1005; Group 2 (outlined in the given figure) contains 12 blocks numbered 2000 to 2011; Group 3 contains 26 blocks numbered 3000 to 3025. Choose a stratified sample of two blocks from the 6 blocks in Group 1, two from the 12 blocks in Group 2, and three from the 26 blocks in Group 3. Choose such a sample by using Table B at line 108 (Give the blocks by the original labeling). Fill in the blanks: The sample is: Group1: block 1) _______ 2) ________. Group 2: blocks 3) _______ , 4) _______ .

Group 3: blocks 5) _______ , 6) _______ , 7) _______ . Answer 1 1000 Answer 2 1004 Answer 3 2007 Answer 4 2009 Answer 5 3006 Answer 6 3000 Answer 7 3015 Score: 8 of 8 6. Step 1: The list of individuals from which a sample is actually selected is called the sampling frame . Ideally, the frame should list every individual in the population, but in practice this is often difficult. A frame that leaves out part of the population is a common source of undercoverage. Suppose that a sample of households in a community is selected at random from the telephone directory. What households are omitted from this frame? What types of people do you think are likely to live in these households? These people will probably be underrepresented in the sample. True or False: Households without telephones are omitted from this frame. However, owning a telephone is not a trait that may have effect on sample results. True False Step 2: The list of individuals from which a sample is actually selected is called the sampling frame . Ideally, the frame should list every individual in the population, but in practice this is often difficult. A frame that leaves out part of the population is a common source of undercoverage. It is usual in telephone surveys to use random digit dialing equipment that selects the last four digits of a telephone number at random after being given

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the area code and the exchange (the first three digits). Which of the households that you mentioned in your answer to (a) will be included in the sampling frame by random digit dialing? True or False: The sample frame by random digit dialing includes also unlisted numbers. These are not included in the sample frame from the telephone directory. True False Score: 2 of 2 7. You are planning a study and are considering taking an SRS of either 300 or 700 observations. Explain how the sampling distribution would differ for these two scenarios. The larger sample would have less sampling variability. Correct The statistics of the smaller sample have more chance for bias than those of the larger sample. The larger sample would have a center closer to the true population parameter. The smaller sample would have less sampling variability. Score: 1 of 1 8. Step 1: For each of the following situations, describe the population and the sample. A survey of 17,096 students in U.S four-year colleges reported that 19.4% were binge drinkers. Population: four-year college students in U.S. Sample: 19.4% of four-year college students in U.S. Population: college students in U.S. Sample: 19.4% of four-year college students. Population: college students in U.S. Sample: 17,096 students. Population: 17,096 students in U.S. Sample: 19.4% of the 17,096 students in U.S.

Step 2: For each of the following situations, describe the population and the sample. In a study of work stress, 100 restaurant workers were asked about the impact of work stress on their personal lives. Determine whether the following statement is True or False: The population is restaurant workers and the sample is 100 restaurant workers. True False Step 3: For each of the following situations, describe the population and the sample. A tract of forest has 584 long leaf pine trees. The diameters of 40 of these trees were measured. The population is the diameters of all long leaf pine trees. The sample is the diameters of 40 long leaf pine trees. The population is long leaf pine trees. The sample is 584 long leaf pine trees. The population is long leaf pine trees. The sample is 40 long leaf pine trees. The population is 584 long leaf pine trees. The sample is 40 of these trees. Score: 3 of 3 9. The given figure shows histograms of four sampling distributions of statistics intended to estimate the same parameter. Label each distribution relative to the others as high or low bias and as high or low variability.

Bias Variability a low high b high low c high high d low low

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Bias Variability a high high b high low c high high d high low Bias Variability a low low b high high c high low d low high Bias Variability a high high b low low c low high d high low Correct Score: 1 of 1 10. Two scientists published a paper claiming to have developed a very exciting new method to detect ovarian cancer using blood samples. When other scientists were unable to reproduce the results in different labs, the original work was examined more carefully. In the original study there were samples for women with ovarian cancer and healthy controls. The serum samples were all analyzed using a mass spectrometer. The control samples were analyzed on one day and the cancer samples were analyzed on the next day. This design was flawed in that it could not control for changes over time in the measuring instrument. True or False: The flaw of the sample can be corrected by alternating between control and cancer samples. False True To control for changes in the mass spectrometer over time, we should alternate between control and cancer samples. Score: 1 of 1

11. A researcher studying the effect of price promotions on consumers' expectations makes up two different histories of the store price of a hypothetical brand of laundry detergent for the past year. Students in a marketing course view one or the other price history on a computer. Some students see a steady price, while others see regular promotions that temporarily cut the price. Then the students are asked what price they would expect to pay for the detergent. Is this study an experiment? Why? What are the explanatory and response variables? This is a sample survey, where the explanatory variable is the price history seen by the subject, and the response variable is the price the subject expects to pay. This is an experiment, since each subject is randomly assigned to a treatment. The explanatory variable is the price the subject expects to pay and the response variable is the price history seen by the subject. This is an experiment, since each subject is randomly assigned to a treatment. The explanatory variable is the price history seen by the subject, and the response variable is the price the subject expects to pay. Correct This study is not an experiment since no treatment is imposed on the subjects. The explanatory variable is the price history seen by the subject, and the response variable is the price the subject expects to pay. Score: 1 of 1

12. Step 1: A drug manufacturer is studying how a new drug behaves in patients. Investigators compare two doses: 5 milligrams (mg) and 10 mg. The drug can be administered by injection, by a skin patch, or by intravenous drip. Concentration in the blood after 30 minutes (the response variable) may depend both on the dose and on the method of administration. Make a sketch that describes the treatments formed by combining dosage and method. Then use a diagram to outline a completely randomized design for this two- factor experiment. A matched pairs design. Choose at random 3 couples. Each couple gets the drug in the same method, one of them gets 5 mg and the other gets 10 mg. Repeat this process several times, each time for other randomly chosen 3 couples. Compare the difference in concentration in blood after 30 minutes within each couple.

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Score: 2 of 2 13. An experiment that favors a certain outcome over other outcomes is called ______. systematic biased Correct favored confounded Score: 1 of 1 14. Which of the following statements best describes the difference between an observational study and an experiment? Without concrete examples, it is not possible to detect what the differences might be. In an experiment the researcher is careful to determine exactly what is to be observed, whereas in an observational study there is greater concern about how the observations are made. In an experiment treatments are deliberately imposed upon individuals and their responses are observed. However, in an observational study without any attempt to influence the responses, individuals are observed and variables of interest are measured. Correct There are really no significant differences between observational studies and experiments. They are different names for essentially the same type of study. In an experiment the data are obtained using careful controls on the treatments, but in an observational study the data are obtained through careful observation of the responses. Score: 1 of 1 15. A medicine to remove the redness in eyes was tested in a group of 100 students. Each student took either the medicine or a placebo in both eyes. The specific treatment for each student was decided by flipping a coin. The participants in the study did not know if heads or tails resulted in the medication. The participants were given some free time after receiving their drops. The researcher did not keep track of what they did in that free time. It turns out that many of the people receiving the medicine spent their time outside and many of the people receiving the placebo spent their time inside. The results could now be biased because the variable location (inside versus outside) is an example of a ___________ variable.

confounding Correct control lurking response Score: 1 of 1

STAT1034 - Ch3 and Ch4 StudyTest

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