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Ask Good Questions: A blog about teaching introductory statistics Post #21: Twenty exam questions Feel free to use and/or modify the following exam questions for use with your students.1. For each of the following quantities, indicate whether it can NEVER be negative or can SOMETIMES be negative. Standard deviationNeverSometimesInter-quartile rangeNeverSometimesz-scoreNeverSometimesCorrelation coefficientNeverSometimesp–valueNeverSometimes2. Consider these two new statistics that we have not yet studied:mid-range = (minimum + maximum) / 2mid-hinge = (lower quartile + upper quartile) / 2Is the mid-range a measure of center or a measure of variability?CenterVariabilityIs the mid-hinge a measure of center or a measure of variability?CenterVariabilityIs the mid-range resistant to outliers? YesNoIs the mid-hinge resistant to outliers?YesNo3. It can be shown that the sum of the residuals from a least squares regression line always equals zero. Does it follow from this fact that the mean of the residuals must equal zero?YesNoDoes it follow from this fact that the median of the residuals must equal zero – yes or no?YesNo4. Suppose that every student in our class scored 5 points lower on the second exam than on the first exam. What would be the value of the correlation coefficient between first exam score and second exam score?-5.0-1.0-0.50.00.51.05.05. Suppose that the observational units in a study are the purchases that I made on in the past 12 months. Identify each of the following as a categorical variable, a numerical variable, or not a variable. Was the purchase shipped to me or to someone else?Categorical variableNumerical variableNot a variableDo I tend to spend more on purchases sent to others than on purchases sent to me? Categorical variableNumerical variableNot a variableHow much did I spend on the purchase? Categorical variableNumerical variableNot a variableDid the purchase include at least one book? Categorical variableNumerical variableNot a variableWhat was the average price of these purchases? Categorical variableNumerical variableNot a variable6. When can you legitimately draw a cause-and-effect conclusion from a randomized experiment? When the p-value is largeWhen the p-value is smallAlways, no matter what the p-value is7. If two numerical variables have a correlation coefficient of 0.93, what can you conclude about whether the variables have a cause-and-effect relationship?There’s definitely a cause-and-effect relationship. There’s definitely not a cause-and-effect relationship. There may or may not be a cause-and-effect relationship.8. Suppose that Brad is preparing to take a multiple-choice exam for which each question has three options, one of which is the correct answer. Brad has a 70% chance of knowing the correct answer (for sure) to a question. If he knows the correct answer, he will definitely answer correctly. But if he does not know the correct answer, he’ll guess randomly among the three options. In the long run, what percentage of questions will Brad answer correctly on such an exam?Less than 70%Exactly 70%More than 70%9. If an experienced and highly accurate meteorologist predicts that there’s a 70% chance of rain in SLO on Saturday and a 30% chance of rain in SLO on Sunday this weekend, is it reasonable to conclude that there’s a 100% chance that it rains in SLO at some point during the weekend?YesNo10. Suppose that 80% of Cal Poly students were born in California and 40% of Cal Poly faculty were born in California. There are more than ten times as many students as faculty at Cal Poly. If we combine Cal Poly students and faculty together, what percentage were born in California?More than 60%Exactly 60%Less than 60%11. If a couple has two children, how confident can they be that one will be a girl and one will be a boy? They can be certain of this. They cannot be certain, but this is very likely. There’s about a 50% chance of this. This is extremely unlikely.12. Suppose that the weights of candy packages follow a normal distribution and that the advertised weight falls below the mean. Suppose also that the manufacturer wants to make a change that will decrease the percentage of candy packages that weigh less than the advertised weight. If they change only the advertised weight, should they make the advertised weight smaller or larger?SmallerLargerIf they change only the mean of the distribution of weights, should they make the mean smaller or larger?SmallerLargerIf they change only the standard deviation of the distribution of weights, should they make the standard deviation smaller or larger?SmallerLarger13. Suppose that you select a simple random sample of 200 houses currently for sale in Los Angeles County. Does the Central Limit Theorem establish that the distribution of the house prices would be approximately normal?YesNo14. The United States has about 330 million residents. Suppose that you want to estimate the proportion of Americans who have a tattoo to within a margin-of-error of 3.5 percentage points with 95% confidence. About how many people would you need to randomly sample? Select the best answer from the following choices.100100010,000100,0001,000,00010,000,00015. Consider a confidence interval for a population mean or a population proportion. Assuming that all else remains unchanged, which of the following would produce a narrower confidence interval?Larger sample sizeLarger confidence levelBoth of the aboveNeither of the above16. As a p-value gets smaller, what happens to the strength of evidence against the null hypothesis?Less strongSame strengthMore strong17. Consider the hypotheses in a hypothesis test.Is a null hypothesis a statement about a parameter or a statistic?ParameterStatisticCould be either, depending on the contextIs an alternative hypothesis a statement about a parameter or a statistic? ParameterStatisticCould be either, depending on the context18. Suppose that you want to compare the percentage of students at Cal Poly – San Luis Obispo (SLO) who wear clothing that says “Cal Poly” to the percentage of students at Cal Poly – Pomona who wear such clothing. You and a friend collaborate to select random samples of Cal Poly students at each campus on a particular day.Which of the following results provides the strongest evidence that the percentages differ between the two campuses? 40 of 100 students at SLO wear Cal Poly clothing, compared to 10 of 100 students at Pomona35 of 100 students at SLO wear Cal Poly clothing, compared to 15 of 100 students at Pomona30 of 100 students at SLO wear Cal Poly clothing, compared to 20 of 100 students at PomonaWhich of the following results provides the strongest evidence that the percentages differ between the two campuses? 4 of 10 students at SLO wear Cal Poly clothing, compared to 1 of 10 students at Pomona20 of 50 students at SLO wear Cal Poly clothing, compared to 5 of 50 students at Pomona40 of 100 students at SLO wear Cal Poly clothing, compared to 10 of 100 students at Pomona19. Suppose that you use sample data to conduct a two-sided hypothesis test of whether two population means differ. The p-value turns out to be .087. What can you say about a 95% confidence interval for the difference in population means, calculated from the same sample data?Include only negative values Includes both positive and negative valuesInclude only positive values 20. Relative risk is defined to be the ratio of success proportions between two groups. Suppose that a 95% confidence interval for a relative risk turns out to be (1.32 2.62). Would you conclude that the sample data provide strong evidence that the success proportions in the two groups differ, and why?Yes, because the confidence interval is entirely greater than zeroYes, because the confidence interval is entirely greater than oneNo, because the confidence interval is entirely greater than zeroNo, because the confidence interval is entirely greater than one21. How has the percentage of the world’s population living in extreme poverty changed over the past twenty years?DoubledRemained more or less the sameHalved ................
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