Math 17 Section 02 Second Midterm Exam Practice

Name: Math 17 Section 02/– Introduction to Statistics Second Midterm Exam PRACTICE Instructions: 1. Show all work. You may receive partial credit for partially completed problems. 2. You may use calculators and a one-sided sheet of reference notes, as well as the provided tables (standard normal, t). You may not use any other references or any texts. 3. You may not discuss the exam with anyone but me. 4. Suggestion: Read all questions before beginning and complete the ones you know best first. Point values per problem (separate page for each) are displayed below if that helps you allocate your time among problems. 5. You may use the back of the first sheet for scratch work or if you run out of space (this is for the 2 sections where you compute test statistics, or if you want to draw a picture of your p-value, etc.). If you leave an answer to a part of a question there, be sure it is clearly marked for me to see. 6. Use 4 decimal places for calculations involving proportions. 7. Good luck! Problem 1 2 3 4 Total 12 13 10 15 50 Points Earned Possible Points 1. Park rangers collect data for various scientific studies. A study focusing on bears involved tagging and recapturing bears over several years in order to track weight (in kilograms) and length (in centimeters) for juvenile female bears as they matured into adults. Rangers tracked 7 bears for 5 years. Focusing on data collected for bears in their second year, they reported a sample mean of 61.14 kg and sample standard deviation of 8.17 kg. The data has been summarized with a qqplot at right. a. Suppose the rangers are about to capture an 8th juvenile female bear in her second year. They want to estimate the weight of the bear, as an average female bear, based on their collected data. Provide the rangers with an interval of possible weights using a confidence level of 98%. Be sure to comment on any assumptions. b. What is value of the standard error of the sample mean year 2 female bear weights? Interpret this standard error. c. The rangers hypothesize that the mean weight is less than 68 kg. Does your confidence interval support their hypothesis? Provide an appropriate conclusion. At what significance level can you make your conclusion? d. What type of mistake could you have made in your hypothesis test? Type I Type II 2. Biologists studying snakes examined 28 male and 28 female anacondas to study gender differences in snout-vent length and weight. The anacondas were captured in the wild during a summer field study. They sorted the anacondas of each gender by snout-vent length (smallest to largest) after the data was collected. The biologists want to use a confidence interval to estimate the difference in snout-vent lengths (SVLs) between genders. a. What parameter is appropriate for this situation? Choose one and explain briefly. d 1 −  2 b. What conditions need to be satisfied for the confidence interval to be valid in this case? What graphs would you need to make (if any) to check these conditions? Be specific. c. Assume the conditions are satisfied. The analyst runs multiple analyses, not knowing which to use. Using the provided partial Rcmdr output, provide the appropriate 90% CI for your parameter in a. My CI is: ___________________________________________________________ Paired t-test (female – male) t = 12.9835, df = 27, p-value = 4.008e-13 alternative hypothesis: true difference in means is not equal to 0 90 percent confidence interval: 103.8415 135.2013 Welch Two Sample t-test (female – male) t = 8.7597, df = 32.708, p-value = 4.316e-10 alternative hypothesis: true difference in means is not equal to 0 90 percent confidence interval: 96.42418 142.61868 d. The multiplier for your confidence interval was based on what distribution? (Be specific). e. Interpret the 90% confidence level used in your confidence interval. f. True/False. Choose one for each statement below. ______ i. Using the same data but increasing the confidence level will result in a smaller margin of error. ______ii. To increase power in a hypothesis test, one option is increasing the sample size. ______iii. The probability your 90% confidence interval contains the difference in population mean SVLs is .90. ______iv. Having a large random sample for females would allow us to conclude that the sampling distribution of the population mean female snout-vent length was approximately a normal distribution. 3. Name that Scenario – For each scenario, determine and define the parameter of interest and determine if a hypothesis test or confidence interval is most appropriate. If you choose hypothesis test, provide the null and alternative hypothesis. All research questions involve the data collected by the US Forest Service and US Geological Survey related to areas of Roosevelt National Forest in Colorado. a. Research question: Investigators want to compare the elevations of forest sites with species of spruce versus elevations of forest sites with species of aspen to see how much of a difference in elevation there is. b. Research question: Investigators focusing on the Neota wilderness area want to know whether or not the majority of sites in the area have the species: ponderosa pine. c. Research question: Investigators want to know if sites in the Rawah region are closer to fire ignition points than the sites in Comanche Peak but also want to control for elevation. So, they selected sites from the Rawah and Comanche Peak wilderness areas based on comparable elevations (site selected from Rawah and then comparable site selected from Comanche Peak) in order to compare their distances to fire ignition points (measured in meters). d. Research question: Investigators want to know what the difference is between the Rawah and Neota regions in terms of the percentages of sites with the species: lodgepole pine. e. Research question: The researchers know that the overall average elevation of forest sites in the Roosevelt National Forest (where these sites are located) is 2959 meters. The researchers want to know whether or not the Neota region has a higher elevation than the whole region, so they sample sites in that region and record their elevations in meters. 4. Investigators studying the Rawah and Neota areas of the Roosevelt National Forest in Colorado have collected a data set of binary variables (0 or 1 – absence or presence) regarding various characteristics of the forests. One characteristic of interest is the presence or absence of soil of an unspecified but unique type (that’s what the study description says!). A graduate student thinks that the Neota forest area will have a lower percentage of this soil type compared to the Rawah area. A random sample of sites from both areas yields the following information: out of 260796 sampled Rawah sites, 2140 have this soil type and out of 29884 sampled Neota sites, 117 have this soil type. a. Set up appropriate hypotheses and any parameter definitions needed to test the graduate student’s belief. b. What is your best estimate of the common proportion of forest area sites that have this soil type? c. Check conditions and perform the mechanics necessary to test the graduate student’s belief. Test stat: p-value: d. What model did you use in order to calculate your p-value? (Be specific). e. Interpret your test statistic. f. What decision and conclusion do you reach at a significance level of .01? Reject H0 Conclusion: Do not reject H0 g. Is your result statistically significant? Is your result practically significant? Explain briefly.