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Soc 380: Elementary Statistics and Data Analysis 4. The number of undergraduates at Duke University is approximately 6500, while the number at KU is approximately 20,800. A simple random sample of 1% of undergraduates at Duke University will be used to estimate the mean number of cigarettes smoked per week for all Duke students. A simple random sample of 1% of undergraduates at the University of Kansas will be used to estimate the mean number of cigarettes smoked per week for all University of Kansas students. Assume the populations have similar standard deviations. What can we conclude about the sampling variability for the sample mean from Duke as compared to that from KU? (2 points) a) The distribution of the sample mean from Duke will have less sampling variability than that from KU. b) The distribution of the sample mean from Duke will have more sampling variability than that from KU. c) The distribution of the sample mean from Duke will have about the same sampling variability as that from KU. d) It is impossible to make any statements about the sampling variability of the two samples because the students surveyed were different. 5. The number of undergraduates at Duke University is approximately 6500, while the number at KU is approximately 20,800. A simple random sample of300 undergraduates at Duke University will be used to estimate the mean number of cigarettes smoked per week for all Duke students. A simple random sample of 300 undergraduates at the University of Kansas will be used to estimate the mean number of cigarettes smoked per week for all University of Kansas students. Assume the populations have similar standard deviations. What can we conclude about the sampling variability for the sample mean from Duke as compared to that from KU? (2 points) a) The distribution of the sample mean from Duke will have less sampling variability than that from KU. b) The distribution of the sample mean from Duke will have more sampling variability than that from KU. c) The distribution of the sample mean from Duke will have about the same sampling variability as that from KU. d) It is impossible to make any statements about the sampling variability of the two samples because the students surveyed were different. 6. Suppose the actual mean number of cigarettes smoked per week for all KU Undergraduates is 2.4 with a standard deviation of L]. What is the mean and standard deviation ofthe sampling distribution of the mean number ot'cigarcttes smoked in repeated simple random samples ot'50 KU undergraduates? (4 points) 7. For the total population ofa small southern city, mean household income is $34,000, with a standard deviation of$5,000. Note: The individual units ofanalysis in this problem are households and the variable of interest is household income. a. How many households would you have to sample to reduce the standard deviation of the sample mean to $255? (4 points) b. What is the probability that a randomly selected household from this city has an income lessthan $32,500? (4 points; don't forget picture and sentence) c. If you take a sample of 50 households from this city, what is the probability that the mean household income in your sample is less than $32,500? (5 points; don't forget picture and a sentence)