1. True or False. Justify for full credit. (a) A is an event, and Ac is the complement of A, then P(A AND Ac ) = 0. (b) If the variance of a data set is 0, then all the observations in this data set must be zero. (c) If a 95% confidence interval for a population mean contains 1, then the 90% confidence interval for the same parameter must contain 1 (d) When plotted on the same graph, a distribution with a mean of 40 and a standard deviation of 10 will look more spread out than a distribution with a mean of 50 and standard deviation of 5. (e) In a two-tailed test, the value of a test statistic is 2. The test statistic follows a distribution with the distribution curve shown below. If we know the shaded area is 0.03, then we have sufficient evidence to reject the null hypothesis at 0.05 level of significance. 2. Choose the best answer. Justify for full credit . (a) A study was conducted at a local college to analyze the average GPA of students graduated from UMUC in 2015. 100 students graduated from UMUC in 2015 were randomly selected, and the average GPA for the group is 3.5. The value 3.5 is a (i) statistic (ii) parameter (iii) cannot be determined (b) The hotel ratings are usually on a scale from 0 star to 5 stars. The level of this measurement is (i) interval (ii) nominal (iii) ordinal (iv) ratio (c) On the Election Day, UMUC News Club organized an exit poll in which specific polling stations were randomly selected and all voters were surveyed as they left those polling stations. This type of sampling is called: (i) cluster (ii) convenience (iii) systematic (iv) stratified 3. Choose the best answer. Justify for full credit. (a) A study of 10 different weight loss programs involved 500 subjects. Each of the 10 programs had 50 subjects in it. The subjects were followed for 12 months. Weight change for each subject was recorded. You want to test the claim that the mean weight loss is the same for the 10 programs. What statistical approach should be used? (i) t-test (ii) linear regression (iii) ANOVA (iv) confidence interval (b) A STAT 200 instructor teaches two classes. She wants to test if the variances of the score distribution for the two classes are different. What type of hypothesis test should she use? (i) t-test for two independent samples (ii) t-test for matched samples (iii) z-test for two samples (iv) F- test 4. A random sample of 100 students was chosen from UMUC STAT 200 classes. The frequency distribution below shows the distribution for study time each week (in hours). (Show all work. Just the answer, without supporting work, will receive no credit.) Study Time (in hours) Frequency 0.0 - 4.9 5 5.0 - 9.9 13 10.0 - 14.9 15.0 -19.9 Relative Frequency 0.22 42 20.0 - 24.9 Total 100 (a) Complete the frequency table with frequency and relative frequency. Express the relative frequency to three decimal places. (b) What percentage of the study times was at least 15 hours? (c) Does this distribution have positive skew or negative skew? Why or why not? 5. The five-number summary below shows the grade distribution of a STAT 200 quiz for a sample of 1000 students. Answer each question based on the given information, and explain your answer in each case. (a) What is the interquartile range in the grade distribution? (b) Which score band has the fewest students? (i) 20 - 60 (ii) 60 - 75 (iii) 75 - 90 (iv) Cannot be determined (c) How many students are in the score band between 75 and 100? Problem Number Solution Answer: (a) (b) (c) (d) 1 (e) Justification: Answer: (a) (b) (c) 2 Justification: Answer: (a) (b) 3 Justification: Answer: (a) Study Time (in hours) Frequency Relative Frequency 0.0 - 4.9 5.0 - 9.9 10.0 - 14.9 5 13 0.22 15.0 -19.9 42 20.0 - 24.9 Total 4 (b) (c) Work for (a) and (b): 100 Answer: (a) (b) 5 (c) Justification