1. For each of the bold items state whether it is a statistic or a parameter. (1.5 points each) a. b. The median age of Americans in the 2000 census was 35.3 years. Using data from the 60,000 respondents to the Current Population Survey the unemployment rate for US. adults is reported to be 9.5%. The percentage of students at KU who receive some form oi'tinancial aid is 55%. You asked 50 people in Fraser Hall if they received some form of nancial aid and only 34%said yes. 2. Match the symbols with the denitions (1.5 points each) re.\" 9-957?\" The standard deviation for a sample. The standard deviation for a sample mean (sampling distribution) The standard deviation for a population. The mean for a sample mean (sampling distribution). The mean for a population. The mean for a sample. if ii. 3 iii. u iv. 0 V. It); vi. a); 3. True or False (2 points each) Most sampling distributions of x-bar are approximately normal when n>=lO, even when the population distribution for variable X is skewed. There is less variability in the means you calculate from small samples compared to the means you calculate from larger samples. An unbiased statistic will sometimes fall above or below the actual parameter. A sampling distribution shows us the distribution ofvalues ofX for a single sample. The difference between a statistic and a parameter is called population error. The population distribution shows us the distribution of values of X for the population. A sample distribution shows us the distribution ofxbar for all possible samples of size n from the population. TF TF TF TF TF TF TF a. 9' (Fi-\"PP.\" 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)