You must complete the midterm
by Friday. Once you begin the midterm, you will have 90 minutes to complete it. The midterm is open book and open note
Page 1 Practice Midterm Choose the best answer for the following: 1. Which measure(s) of central tendency can be applied to nominal data? a. The mean b. The median c. The mode 2. The sampling distribution for the mean is a. only normally distributed for small samples. b. the theoretical distribution of all means in all samples that we could draw from our population. c. a distribution that we must directly observe in order to conduct a hypothesis test. d. a marketing scam involving the distribution of “free” samples. 3. A Gallup poll on the Presidential race several weeks before the 2012 election showed that 49% of likely voters planned to vote for Obama. The margin of error was +/- 2%. Which of the following statements is true? a. 95% of samples that are drawn from all political polls showed Obama with less than 50% of the support of likely voters. b. 95% of the time, likely voters will vote for the candidate that they support in a poll. c. With 95% confidence, we can estimate that among all likely voters in the U.S., between 47 – 51% would have voted for Obama if the vote were held when the poll was taken. d. If the election were held when the poll was taken, Obama would have lost because his support among likely voters was less than 50%. 4. We are interested in gender differences (using just the gender binary, unfortunately) in work outside of the home, so we produce the following SPSS output from the GSS 2018. Answer the following: a. Who has the highest mean number of hours, men or women? b. Which group has the great variation around the mean, men or women? Page 2 5. A police department concerned with levels of white collar crime is interested in the number of years the typical offender works for a company before being caught for engaging in financial crimes against their employer. The department has hired a researcher to assess this relationship. She finds that in a sample of 25 convicted criminals, they report a mean of 14 years with their employer with a standard deviation of 5. Construct a 95% confidence interval for the mean number of years employed, and then provide an interpret of this confidence interval. 6. A random sample of 175 people surveyed were asked whether or not they support the death penalty. Seventy-five percent responded that they do not. Estimate the population proportion with a 95% confidence interval. 7. You are interested in whether those who pay attention to local news express a greater fear of crime than those that don’t (forget, for a moment, that there are other ways to get news than the old- fashioned newspaper). You produce the following frequency distribution from the General Social Survey. Answer the following: a. What value of N should you use to formulate a confidence interval for the proportion who say they read the newspaper every day? Be careful – don’t provide the frequency of those who read everyday here. b. What is the level of measurement for this variable? c. What percentage of valid responses report that they read the paper every day? d. What percentage read the paper at least a few times a week. Find the 95% confidence interval for each of the following: 1. Estimate the standard error of the mean with the following sample of 30 responses on a 7-point scale, measuring whether an extremist hate group should be given a permit to demonstrate (1- strongly oppose through 7-strongly favor)*. The sample mean is 3.3 with a standard deviation of 1.56. 2. In order to estimate the proportion of students on a particular campus who favor a campuswide ban on alcohol, a researcher interviewed a random sample of 25 students from the college population. She found that 36% of the sample favored banning alcohol. 3. A polling organization interviewed by phone 400 randomly selected adults in New York City about their opinion on random drug testing for taxi drivers and found that 38% favored such a regulation. 4. A major research organization conducted a national survey to determine what percent of Americans feel that they are more or less likely to become a crime victim now than they were five years ago. Asking 1,200 randomly selected respondents if their feeling of safety had improved over the past five years, 45% reported that they feel less safe. 5. To determine the views of students at a particular college about campus security, an 11-point attitude scale was administered to a random sample of 40 students. This survey yielded a sample mean of 6 (the higher the score, the higher the perceived effectiveness of security measures) and a standard deviation of 1.5. Find the 95% confidence interval. 6. A local police department attempted to estimate the average rate of speed (X) of vehicles along a strip of Main Street. With hidden radar, the speed of a random selection of 25 vehicles was measured, which yielded a sample mean of 42 mph and a standard deviation of 6 mph * Note that some of these variables are measured at an ordinal level but we are treating them as interval/ratio for these problems. Page 1 Practice Midterm Answer Key Choose the best answer for the following: 1. Which measure(s) of central tendency can be applied to nominal data? a. The mean b. The median c. The mode 2. The sampling distribution for the mean is a. only normally distributed for small samples. b. the theoretical distribution of all means in all samples that we could draw from our population. c. a distribution that we must directly observe in order to conduct a hypothesis test. d. a marketing scam involving the distribution of “free” samples. 3. A Gallup poll on the Presidential race several weeks before the 2012 election showed that 49% of likely voters planned to vote for Obama. The margin of error was +/- 2%. Which of the following statements is true? a. 95% of samples that are drawn from all political polls showed Obama with less than 50% of the support of likely voters. b. 95% of the time, likely voters will vote for the candidate that they support in a poll. c. With 95% confidence, we can estimate that among all likely voters in the U.S., between 47 – 51% would have voted for Obama if the vote were held when the poll was taken. d. If the election were held when the poll was taken, Obama would have lost because his support among likely voters was less than 50%. 4. We are interested in gender differences (using just the gender binary, unfortunately) in work outside of the home, so we produce the following SPSS output from the GSS 2018. Answer the following: a. Who has the highest mean number of hours, men or women? b. Which group has the great variation around the mean, men or women? See the standard deviation. It is larger for men (14.969) than for women (13.276), illustrating greater dispersion or variation around their respective means for men. Page 2 5. A police department concerned with levels of white collar crime is interested in the number of years the typical offender works for a company before being caught for engaging in financial crimes against their employer. The department has hired a researcher to assess this relationship. She finds that in a sample of 25 convicted criminals, they report a mean of 14 years with their employer with a standard deviation of 5. Construct a 95% confidence interval for the mean number of years employed, and then provide an interpret of this confidence interval. In solving confidence interval problems, make sure you first determine if it’s a confidence interval for a mean or for a proportion. A mean problem will provide the standard deviation (s), a proportion problem will not, and may be expressed as a percentage instead of a proportion. This is a means problem. df = N-1 = 25-1 = 24, so t = +/- 2.064 (Reminder: use the t-table in Appendix C, Table C to identify this value of t. Use .05 as the level of significance, and make sure you’re using the two-tailed test table, not the one-tailed test on the following page.) ?�̅� = ? √? − 1 = 5 √24 = 5 4.9 = 1.02 �̅� ± ?(?�̅�) = 14 ± 2.054(1.02) = 14 ± 2.1 OR 11.9 to 16.1 We are 95% confident that among all convicted white collar criminals, the mean number of years working for their employer falls between 11.9 and 16.1 years. Note the italicized phrase above -- all convicted white collar criminals. The confidence interval always refers to an interval estimate of the larger population, not the sample that is drawn from that population. We already know the mean for the sample; our interval estimate is for the larger population from which the sample is drawn. 6. A random sample of 175 people surveyed were asked whether or not they support the death penalty. Seventy-five percent responded that they do not. Estimate the population proportion with a 95% confidence interval. z = +/- 1.96 for 95% confidence interval for a proportion ?? = √ .5(1−.5) 175 = √ .25 175 = √. 0014 = 0.038 NOTE: remember that we always use .5 in the numerator for this formula. This is different from the book!! 95% confidence interval: 0.75 +/- 1.96(.038) = 0.75 +/- .074 or 75% +/- 7.4% or 67.6% to 82.4% With 95% confidence, we estimate that between 67.6% and 82.4% of the entire population supports the death penalty. Page 3 7. You are interested in whether those who pay attention to local news express a greater fear of crime than those that don’t (forget, for a moment, that there are other ways to get news than the old- fashioned newspaper). You produce the following frequency distribution from the General Social Survey. Answer the following: a. What value