Stat 135 Final Exam Fall 2016

Stat 135 Final Exam \ NAME: . You must show all work, calculations, formulas used to receive any credit. NO WORK =NO CREDIT. Round the final answers to 3 decimal places. Good luck! Question 1 Question 2 Question 3 Question 4 Question 5 Question 6 Question 7 Total out of 100. Fall 2016 1. General Question. Several scenarios are listed below on the left. For each scenario, list the statistical method you should use. Not all of the procedures listed will be used.   A health professional selected a random sample of 100 patients from each of four major hospital emergency rooms to see if the major reasons for emergency room visits are similar in all four major hospitals. The major reason categories are accident, illegal activity, illness, and other. _______ A study wanted to examine the relationship between number of Japanese beetle grubs and percentage of organic matter in the soil for locations on a golf course in New York.. _______  A study compared the toxicity on flies of four different types of selenium. The number of dead flies was counted and the selenium type (type 1, 2, 3, or 4) was recorded for each observation. The researchers want to know if the toxicities differ between selenium types _______  You’d like to see if there is a difference in the mean incoming SAT score of incoming freshmen among all of the five colleges _______  A food distributor wants to know if new robots being used to fill the 8 oz. pasta packages in a pre-packaged food kit are overfilling the packages _______              One-sample t-Interval for a mean Two-sample t-Interval for a mean One-sample z-Interval for a proportion Two-sample z-Interval for a proportion Matched pairs t-Test One-sample t-Test for a mean Two-sample t-Test for a mean One-sample z-Test for a proportion Two-sample z-Test for a proportion ANOVA Linear regression Chi-squared test for homogeneity Chi-squared test for independence 2. A biologist studying lizards, specifically Cophosaurus texanus, recorded the weight (mass) in grams, snout-vent length (SVL) and hind limb span (HLS) of a random sample of 25 such lizards. The biologist wants to study the relationship between variables, looking to see if SVL can be used to predict weight (mass) accurately. a. Based on the scatterplot, how would you describe the relationship between SVL and mass? A student working in the biologist’s lab runs a regression analysis on the data and produces the following partial R output: Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -13.51551 1.22931 -10.99 1.24e-10 *** SVL 0.32459 0.01786 18.18 3.84e-15 *** --Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 0.6986 on 23 degrees of freedom Multiple R-squared: 0.9349, Adjusted R-squared: 0.9321 F-statistic: 330.5 on 1 and 23 DF, p-value: 3.836e-15 b. What is the value of the sample correlation coefficient? Interpret the correlation coefficient. c. Interpret the R-squared value. How well you think this model fits the data? d. What is the equation of the least squares regression line e Check the assumptions . f. Now , we want to assess whether or not SVL can be used to predict mass (weight) .What hypotheses correspond to determining if SVL is a significant predictor Null hypothesis: Test Statistic: Distribution of Test Stat: p-value (how to calculate) Conclusion: Alternative Hypothesis : g. Obtain a 95% confidence interval for the population slope. (You do not need to list assumptions.) . Interpret your interval Can you conclude the population slope is less than 1? Explain. h. Obtain predictions for mass based on SVLs of 64 and 98, if appropriate. If inappropriate, explain why. j. Which of the following aspects of the scatterplot affect the standard error of the regression slope? A. spread around the line: s e B. spread of the x values: s x C. sample size: n D. all of the above 3, A January 2010 article discusses relationships between organochlorine pesticide exposure and a variety of other variables, trying to focus on cancer rates. One extraneous variable included was education level, and we want to see if there is a relationship between exposure to oxychlordane (a selected pesticide) and education level. Summary information from this representative study is shown in the table. a. What is the appropriate inference procedure to determine if there is a relationship between oxychlordane level and education level? (Be specific).List the conditions for your test procedure.. b. Assuming the conditions for inference check out, the appropriate test statistic is 62.122. What distribution does the test statistic have assuming the null hypothesis associated with your selection in a. is true? c. What can you say about the numerical value of your p-value? d. Give your conclusion in context at a .03 significance level. 4.Researchers studying salmon in the Pacific Northwest collected a data set with the diameter of growth rings for first year freshwater growth (hundredths of an inch) and type of salmon (1= Alaskan females, 2= Alaskan males, 3= Canadian females, 4= Canadian males) along with some other variables for a random sample of salmon. The researchers want to know if there are differences in the average diameter of these growth rings for the four different types of salmon. They decide to run an ANOVA to address that research question. Some preliminary analysis and partial ANOVA R output is shown below. Df SumSq Mean Sq Type 38591 12864 Residuals 28338 Type Mean SD n 1 2 3 4 18.34 13.49 17.01 19.24 26 24 26 24 96.58 100.33 139.54 135.21 F value Pr(>F) <2.2e-16 a. (Circle one) This ANOVA is balanced b. What does the preliminary analysis reveal to you? unbalanced. c. In order for this ANOVA to be valid, you need 4 independent random samples which come from normally distributed populations. Assume those assumptions are met. What is the second assumption about the populations? Does it appear to be met? Discuss two different ways of checking it with the output provided. Assumption: Method 1: Method 2: d. Determine the missing values for the degrees of freedom and the test statistic. Type df= F value= Residuals df= Test Null hypothesis: Test Statistic: Distribution of Test Stat: p-value (show how to calculate): Conclusion: Alternative Hypothesis : e. What is your best estimate of the common population variance? f. Compute a 95% confidence interval for µ1 - µ2. 1= Alaskan females, 2= Alaskan males g. Are multiple comparisons appropriate? Explain. If yes, summarize the results. 5. Lizard measurements of mass and snout-vent length (SVL) for 2 genera – Cnemidophorus and Sceloporus - were collected in 1997 and 1999. The primary researcher wants to know whether or not Cnemidophorus has a smaller SVL than Scelophorus, on average. Observations were collected for a random sample of 20 Cnemidophorus and 40 Sceloporus lizards. a. Explain in one sentence why a paired t-test is not appropriate for this data set and research question. b. Set up appropriate hypotheses and parameter definitions to address the researcher’s question. Null: Alternative: c. What is the normality condition related to this inference procedure? In order to check it, what graphs would you need? Explain if having these graphs to check the condition is more important for one genus than the other. Assuming the conditions checked out, the following R output was obtained. The subtraction order was Cneidophorus – Sceloporus. Welch Two Sample t-test data: svl by genera t = 1.5696, df = 48.187, p-value = 0.1231 alternative hypothesis: true difference in means is not equal to 0 mean in group Cnemidophorus mean in group Sceloporus 81.9750 75.9125 d. What is the p-value for your test? e. Interpret your p-value in context. f. Provide an appropriate conclusion at α=0 .1 significance level. 6.Renting a living space is something almost everyone does at some point in their lives. How does the rental atmosphere change if you have AIDS and mention it? A study in 1999 investigated this question by having an adult male caller respond to 2 random samples of 80 advertisements for room for rent. For the first sample, he did not allude to having AIDS, and for the second, he alluded that he was in the hospital, about to be released and needed a place to live. For the first random sample (no AIDS reference), the caller was told a room was available in 61 calls. For the second random sample (AIDS reference), the caller was told a room was available in 32 calls. Is there sufficient evidence to conclude that a reference to receiving treatment for AIDS substantially decreases the likelihood of a room being stated as available? Use a significance level of .01, and be sure to discuss any possible issues with conditions necessary for carrying out the test. a) State hypotheses: b) Assumptions: c) Test statistic p-value computations: . What is the distribution of the test statistic assuming the null hypothesis is true? (Be specific). d) Conclusion: e) . Suppose you had decided to do this test by making a confidence interval. What confidence level for a CI is consistent with performing your test at a .01 significance level? 7. Please answer each of the following using 1-2 sentences. a) Explain, in a linear regression model, why we might want to include an interaction term between two predictors x1 and x2. b) If we created a new model by adding several more explanatory variables, which statistic should be used to compare them – the R2 or the adjusted R2. Explain. c) Which of the following are NOT characteristics of a good regression model? (i) relatively few predictor variables (ii) a relatively high R2 (iii) relatively small p-values for the F – and t-statistics (iv) a relatively low values of s (the standard deviation of the residuals) (v) All of these are characteristics of a good regression model.