2. 

Below there are three sets of numbers, set I, set II, and set III. Each set contains five different numbers. | 38 52 45 55 35 || 120 106 123 113 103 Ill 1984 1998 1991 2001 1981 For each set of numbers you can get its variance: Var(set I), Var(set II), and Var(set III). Order the variances according to its numerical value. Select one: 0 a. Var(set I) > Var(set ll)>Var(set Ill) b. Var(set I) = Var(set II) > Var(set III) C. Var(set I) = Var(set II) 300,000 d. H041: 315,000 vs.H1:u >315,000 0000 e. H01u= 300,000 VS.H1:u= 300,000 Which of the following statements is false? Select one: 0 a. the mean is greater than the median when a distribution is skewed to the right. 0 b. the mode is greater than the mean when a distribution is skewed to the left. 0 c. For a symmetric distribution, the mode is equal to the median. 0 d. The mode changes when we add an extreme value to the left of the distribution. As a real estate agent in the Urbana-Champaign area, you have long made the claim that houses sold in Urbana (population 'I) are generally older than the houses sold in Champaign (population 2). You decide to check whether this claim is statistically valid and assume that the population variances are equal. You collect a sample of ages of houses sold in the two cities, and find the following data: City Sample Size Average Age Standard Deviation Urbana 24 46 18 Champaign 35 42 16 What is the value of the test statistic for testing whether the average age of houses is equal in Urbana and Champaign? Select one: Q a. 3.6784 0 b. 3.6815 0 c. 3.6407 0 d. 0.8965 0 e. 0.8768 Which of the following is not a measure of dispersion? Select one: 0 a. Range 0 b. Median O c. Quartile deviation 0 d. Coefficient of variation ABC, a computer manufacturer claims that their ultra light notebook's battery can last 20 hours or less. After buying the notebook, you notice that the battery lasts more than 20 hours and you want to test their claim. You take a random sample of 50 notebooks and find that on average, the notebook battery lasts 22 hours. From consumer reports, you know that the population standard deviation is 5.2 hours. What sample size would be needed to form a 90% Confidence interval with a width of 0.6? Refer to the following critical values. 2001 = 2.326 Zo_025 = 1.960 2005 = 1.645 201 =1.282 t031,49 = 2-405 t0025,49 = 2-010 t(105,49 = 1-676 to_1,49 = 1.299 Select one: Q a. n=203 O b. n=305 O c. n=503 0 d. n=945 You believe that the quality of the companies appearing on Shark Tank has increased over time. You obtain data on average sales for a random sample of 20 companies that appeared on the show in Season 6 and found that the average was $315,000 with a standard deviation of $40,000. You are told that the average sales for all companies appearing on Shark Tank in Season 1 was $300,000. Have average sales increased since Season1. What is the appropriate test shall we use? Select one: 0 a. ztest b. z-test with degree of freedom 19 c. t-test with degree of freedom 20 d. t-test with degree of freedom 19 0000 e. none of above A congressional subcommittee considering regulation of the cable television industry investigates whether cable rates are higher, on average, in areas with no competition (population 1) than in areas with competition (population 2). They randomly sample the basic rates for six cable companies that have no competition and for six companies that face competition. Sample descriptive statistics are shown below. Assume that population variances are NOT equal. No Competition Competition Mean 24. 14 Mean 20.88 Standard deviation 2.17 Standard deviation 3.36 What is the value of the test statistic for this hypothesis test Select one: Q a. 0.653 O b. 1.996 O c. 3.357 Q d. 3.396 0 e. 1.223 Which of the following is true for a distribution that is skewed to the left? Select one: 0 a. MeanMedianzMode Let's say you work as an administrative person at UIUC. Right now you are interested in knowing whether at least 75% of the university students have used the library over the last week' Which of the following statistical tests is best suited for this purpose? Select one: Q a. A t-test for a single population mean 0 b. A z-test for a single population mean 0 c. A ztest for a single population proportion Q d. A t-test for a single population proportion 0 e. A z-test for the difference in population proportions A producer of low-calorie protein bars wants to test if the product makes consumers eat fewer calories at lunch, so he can use this claim to improve the image of the product and get more clients. According to his advisors, people that eat these bars as morning snacks consume on average fewer calories than people who do not eat them. To have evidence that supports this claim, the company interviewed 200 people including 115 consumers and 85 non- consumers of the protein bars. They collected information about the number of calories each person consumed at lunch. The collected data shows that the consumers of the protein bars eat on average 653 calories at lunch, and the non-consumers eat on average 650 calories at lunch. Moreover, the variance for the caloric consumption at lunch among consumers is 9923 and among non-consumers is 10575. The value of the test statistics for difference in means that they get with the data is 0.207. With the information given in this problem, what is the p-value in this case and what can you conclude? (Use the appropriate Excel function and assume unequal population variances). Select one: 0 a. p-value=0.054. Reject Ho and conclude that consumers of the low-calorie protein bars eat fewer calories at lunch. 0 b. p-value=0.418. Do not reject Ho. There is not enough evidence to claim that low-calorie protein bars reduce intake of calories at lunch. 0 c. p-value: 0.582. Do not reject Ho. There is not enough evidence to claim that low-calorie protein bars reduce intake of calories at lunch. 0 d. p-value=0.033. Reject Ho and conclude that consumers of the low-calorie protein bars eat fewer calories at lunch. 0 e. p-value=0.836. Do not reject Ho. There is not enough evidence to claim that low-calorie protein bars reduce intake of calories at lunch. Which of the following is true about confidence interval? Select one: O a. We reject null hypothesis if Cl contains 0 O b. We accept null hypothesis if Cl contains 0 O c. We do not reject null hypothesis if Cl contains 0 O d. The uppper bound of Cl is always positive O e. The lower bound of Cl is always negative