Statistics and Data Analysis: Confidence Intervals, Hypothesis Testing, and Correlation, Exams of Statistics

Download Statistics and Data Analysis: Confidence Intervals, Hypothesis Testing, and Correlation and more Exams Statistics in PDF only on Docsity! Stat 135 Practice Final Exam Name (300 points total) T.A. Instructor *** True or False (5 points each - no need to explain) True 1) A test statistic is used to measure the difference between the observed sample data and what is expected when the null hypothesis is true. True 2) If a value has a standard score of –1.8 then it must be below the mean. False 3) A boxplot will quickly show if a distribution is bimodal. True 4) Most of the students in last quarter's statistics 135 class, that responded to a survey, did not smoke, although one student smoked three packs a day. True or False: For this group of students the mean number of cigarettes smoked per day was larger than the median. True 5) Two newspapers report the results of the same Gallup Poll regarding the percentage of people who favor term limits for Senators. The first newspaper uses the poll to present a 95% confidence interval for this percentage, while the second newspaper presents an 80% confidence interval. True or False: The confidence interval presented by the first newspaper will be wider than the interval reported by the second paper. True 6) If everyone who works at a restaurant is given a $500 holiday bonus then the correlation between their individual incomes and hours worked would not change. False 7) If the P-value is 99.999% then the null hypothesis does not provide a plausible explanation for the data. False 8) If a list of numbers has a mean of 0, then the standard deviation will also be zero. True 9) You are more likely to get heads on between 40% and 60% of the tosses when you toss a fair coin 800 times than when you toss the coin 8 times. True 10) One thousand students are randomly selected from the list of those currently registered at Ohio State and they each report how many miles they rode in a COTA bus during the past week. Since many students did not ride a bus at all, a histogram of the values does not look like the normal curve. True or False: Even though the histogram did not follow the normal curve, it is still possible to use the normal distribution to make a confidence interval for the average number of miles that all OSU students rode on COTA buses last week. *** Multiple Choice (10 points each - no need to explain) B 11) One morning a pet store weighed each rabbit it has for sale. The standard deviation of these weights is 2 pounds. A collar that weighs 0.1 pounds is then put on each of these rabbits. The standard deviation of their weights at this point (including the collars) is then: A) 2.1 pounds B) 2 pounds C) 1.9 pounds D) changed by a factor corresponding to the standard units of 0.1 years. C 12) Below is a histogram of the size (length of longest dimension in mm) of ocular tumors seen at the OSU ophthalmology clinic over the past three years. One patient had a tumor that was 1mm in size. Its standard score in this data set A) would follow the normal distribution. B) would be bigger than the median. C) would be a negative number. D) would be a positive number. D 13) Boxes of birthday candles in a shipment weigh an average of 4 ounces with a standard deviation of 0.2 ounces. A histogram of these weights followed the Normal distribution quite closely. Approximately what percentage weighed between 3.78 ounces and 4.22 ounces? A) 4.7% B) 9.3% C) 54.7 % D) 72.9% D 14) A spinner can land in eight possible positions so that all eight have the same probability of coming up. Each position must have probability A) between 0 and 1, but can't say more. B) between -1 and 1, but can't say more. C) 1/2. D) 1/8. D 15) A sample is about to be taken from the 900 students taking Statistics 135 this quarter. Which of the following would most closely follow the normal distribution? A) The histogram of the weights of 2 randomly selected students B) The histogram of the weights of 20 randomly selected students. C) The sampling distribution of the average of the weights of 2 randomly selected students D) The sampling distribution of the average of the weights of 20 randomly selected students *** Matching (no need to explain) 16) (12 points- 4 points each) Match the summary statistics with the histograms i) mean = 6.6, median = 6.8, standard deviation = 1.3 variable 2 ii) mean = 6.6, median = 6.0, standard deviation = 8.65 variable 3 iii) mean = 6.6, median = 3.75, standard deviation = 7.4 variable 1 21) (24 points) A genetic theory says that a cross between two pink flowering plants will produce red flowering plants 25% of the time. To test the theory, 100 crosses are made and 31 of them produce a red flowering plant. Is this strong evidence that the theory is wrong? Carry out the appropriate hypothesis test. Be sure to write down the null and alternative hypotheses, find the test statistic and the P-value, and state your conclusions. Null hypothesis: p=0.25 (where p = the expected proportion of red-flowering plants) Alternative hypothesis: p≠0.25 Test statistic: z = 0.31- 0.25 0.25(0.75)/100 =1.386 P-value ≈ 16% (use Table B and be sure to include the region in both tails) The null hypothesis is a reasonable explanation of the data. Such a large P-value indicates that we don't have strong evidence that the genetic model is wrong. 22) (20) Customers using a self-service soda dispenser take an average of 12 ounces of soda with an SD of 4 ounces. What is the chance that the next 100 customers will take an average of less than 12.24 ounces? The sampling distribution of x with n=100 is normally distributed with a mean of m=12 and a standard deviation of s n = 4 100 = 0.4. Standard score = (12.24 - 12)/0.4 = 0.6 From Table B, the answer is 72.6% 23) (20 points) A researcher at The Ohio State University believes that a certain component of ant venom can be used to lessen the amount of swelling in the knuckles of people suffering from arthritis. The ant venom treatment has been made into a capsule form that can be swallowed. Explain how you would design an experiment to investigate whether this new treatment when taken orally each day for one week causes a lower degree of swelling in arthritis sufferers. (You may suppose that 200 people suffering from arthritis have already volunteered to be experimental subjects). Identify the explanatory variable and the response variable in your experiment. Randomly assign people to ant venom capsule or placebo capsule. At the end of one week, check for an increase or decrease in swelling (be sure the person checking doesn't know which group the subject is in. This would be an example of a randomized, double-blind, comparative experiment. Explanatory variable: whether the subject got ant venom or placebo Response variable: the degree of change in swelling. 24) (12 points) Many polls were taken during the 1996 presidential campaign. Throughout the month of October nearly all of the polls conducted by the major polling organizations showed third party candidate Ross Perot receiving the support of between 5% and 10% of those surveyed. The day after the first debate between President Clinton and former Senator Dole, several polls were taken using the same methodology as previous polls except they were directed only at people who had watched the debate. In these post-debate polls, Ross Perot received the support of between 2% and 3% of those surveyed. The regular polls taken later that week again showed Perot's support in the 5% to 10% range. In estimating the percentage support of all voters for Ross Perot during the month of October, what is the most likely explanation for the difference between these polls taken the day after the debate and the other October polls? Explain. Perot voters were less likely to be watching the debate since their candidate wasn't involved. Thus the polls that only questioned only people who had watched the debates would provide biased estimates of the preferences of all voters. 25) (24 points) A paint manufacturer fills cans of paint using a machine that has been calibrated to fill the cans to contain an average of 1 gallon (128 ounces) each. To test whether their machine has come out of calibration, the manufacturer takes a random sample of 100 cans and finds that they average 128.2 ounces with an standard deviation of 4 ounces. Is this strong evidence that the can- filling machine is set too high and is no longer calibrated properly? Carry out the appropriate hypothesis test. Be sure to write down the null and alternative hypotheses, find the test statistic, the P-value, and state your conclusions. Null hypothesis: m = 128 (where m = long run average put in can) Alternative hypothesis: m > 128 ( m≠128 also okay) Test statistic: z = 128.2 - 128 4 / 100 = 0.5 P-value ≈ 30.85% (or 61.7% if you specify the two-tailed alternative) The null hypothesis provides a reasonable explanation of the data. With such a high P- value, we don't have strong evidence that the machine is out of calibration. 26) (20 points) Customers at a grocery store pay with a credit card, with cash, or with a check. Sixty percent of the customers pay with cash. Eighty percent pay don't use a credit card. What is the probability that a randomly picked customer pays with a check? Explain. Since 80% don't use a credit card, 20% do 100% (all customers) - 60% (chance of cash use) - 20% (chance of credit card use) = 20% (chance of check use) 27) (12 points) Trucks are weighed at a Truck Scale to establish the amount owed in road taxes. Someone complains that the weighing procedure has three problems. Problem I: Sometimes the driver is sitting in the truck when it is weighed. Problem II: When the same truck is weighed independently more than once, the truck scale will give different values. Problem III: When the legislature established the road tax, they intended to tax according to the value of the goods being shipped, not according to the weight. Which of the above indicates (Explain each briefly) a) (4 points) a problem with bias? problem I - when the driver is in the truck the measured weight is systematically higher b) (4 points) a problem with reliability? problem II - reliability deals with the issue of consistency or how much measurements bounce around when independently repeated. c) (4 points) a problem with validity? Problem III - validity deals with the issue of appropriateness for the issue at hand