STP 231 Example FINAL

Transcription

1 STP 231 Example FINAL Instructor: Ela Jackiewicz Honor Statement: I have neither given nor received information regarding this exam, and I will not do so until all exams have been graded and returned. PRINTED NAME: CLASS TIME: Signed Date: DIRECTIONS: This is a closed book examination. You may use a graphing calculator and a 8X11 page with hand written notes, no completely solved problems are allowed (one side only). Turn in the notes with your exam. There are 2 problems (64 points total) where you must show all relevant work and provide complete and well organized answers followed by 6 multiple choice questions (6 points each) for which no work needs to be showing, followed by two extra credit questions (6 points total) for which you are expected to sketch a graph. All computations may be done on the calculator, except when request is made to show all work by hand (in the first two problems) Relax and good luck! PLACE ANSWERS TO MULTIPLE CHOICE QUESTIONS BELOW: Write A D as appropriate QUESTION Question3 Question4 Question5 Question6 Question7 Question8 ANSWER B B A C A A

2 Part1 Show all relevant work on questions 1 and 2, you may use a calculator Question 1(30 points) How to quit smoking? A researcher wanted to find out what is the best method for quiting smoking. Two random samples of smokers were given two different treatments: Nicotine Gum and Nicotine Patch and after 5 months determination was made what was the result: they quit or are still smoking. Data is presented below. Treatment Nicotine Gum Nicotine Patch total Still smoking Quit smoking total At 5% significance level does these data present evidence that Nicotine Gum is more effective than Nicotine Patch in helping smokers quit smoking, or the result is independent of the treatment? Test by means of Chi square test of independence, use appropriate directional hypothesis. (5 points) Formulate both hypotheses. H 0 : Both treatments equally effective H A : Nicotine Gum is more effective (5 points) Compute one expected count in the cell (1,1) (first row, first column ) by hand, clearly show all work. E 11 = 250(443)/570=194.3 (5 points) Partial Test Statistics without a cell (1,1) (first row, first column) included is equal to 7.36, compute a complete Test statistics by adding the missing part, show your work by hand, keep at least 2 decimal places χ 2 s =7.36+ ( )2 = = (10 points) Compute p value, you may give exact value or estimate it from tables. List degrees of freedom and include appropriate sketch. Remember that alternative hypothesis is directional. P value=0.004/2=0.002 Sketch represents a Chi square curve with area shaded right of 8.41 labeled as a p value for nondirectional alternative hypotheses (5 points) Decide if null hypothesis is rejected or not at α=.05, give the reason why, and clearly answer question posed in the problem, use a complete sentence. P value< 0.05, so we reject null hypotheses at 5% significance level,. There is evidence that Nicotine Gum is more effective than Nicotine Patch.

3 Question 2 (34 points) Calories and Cholesterol. The number of calories and cholesterol content (in milligrams) for a random sample of fast food chicken sandwiches from seven restaurants are shown below. You may use a calculator to answer following questions, keep at least 2 decimal places. Restaurant A B C D E F G X= Calories Y=Cholesterol x= s x = y=60.14 s y =11.99 r=0.916 a.(6 points) Calculate least squares regression line of Y on X, write the equation below: y = 0.081X b. (6 points) Interpret the slope of the regression line in the context of the problem. Be very specific. As calories in a sandwich increase by 1, cholesterol content increases by milligrams. c. (6 points)use your equation to predict the cholesterol content in a chicken sandwich with 450 calories (450)=21.32=57.77 milligrams d) (6 points)give percent of total variation in Y that is explained by the regression line? r 2 =0.8391, so 83.91% e) (10 points)assuming the linear model is applicable, test the null hypothesis of no relationship between X and Y against the alternative hypothesis that sandwiches with higher number of calories tend to have higher cholesterol content. Use α=.01. Clearly show all the parts of the hypothesis test, including formulation of both hypotheses. H 0 :ρ=0 (β 1 =0) H 0 :ρ>0 (β 1 >0) 5 t= =5.11 p value=0.0019<0.01, so null is rejected, there is evidence ot 1% significanc elevel that linear trend is positive, sandwiches with higher number of calories tend to have higher cholesterol content

4 Part2: Multiple Choice Questions (6 points each) Use following information for Questions 3 4 Numerical variables X and Y show a linear trend on the scatter plot and we want to obtain the Least Squares Regression line for our data. Question3 Suppose the regression equation is ŷ= x and coefficient of determination is 0.81, then what is the linear correlation coefficient? (A) 0.9 (B) 0.9 (C ) (D) (E) none of these Question4 Suppose linear correlation coefficient (r) is computed, then r = 0.62 suggests a stronger linear relationship than r = (A) Yes (B) No (C ) not enough information Use following information in Questions 5 6 Recreational Reading and Gender. A book store owner wished to determined if there is an association between gender and type of books selected by his customers. He collected a random sample of customers and classified them according to gender (Male, Female) and type of books they selected ( Mystery, Romance, Self-Help, Other). He used Chi-square test of independence. Question5 Suppose that our sample had 75% of females and 25% of males. If type of books selected were independent of sex we would expect roughly three quarters of each type of books to be selected by females and roughly a quarter selected by males. (A) True (B) False (C) Not enough information to determine Question 6 Suppose our researcher received a test statistics χ 2 =12.3. Compute p-value (round answer to 3 decimal places) and decide which of the following statements is true? Select one from the following: (A) p value = 0.006, H 0 is rejected, there is no evidence of association at α=0.01 (B) p value = 0.015, H 0 is not rejected, there is evidence at of association at α=0.01 (C) p value = 0.006, H 0 is rejected, there is evidence of association at α=0.01 (D) p value = 0.015, H 0 is not rejected, there is no evidence of association at α=0.01 Question7 Supppose p=proportion of smokers in the Arizona. A random sample of 56 AZ residents revieled that 16 of them are smokers. Obtain margin of error in 95% confidence interval for p, use p tilde ( ~ p) as your estimate of p. Give 3 decimal places for your final answer. (A) (B) (C ) (D) Question8 Suppose 95% confidence interval for the difference between proportions of smokers in the USA and Poland is ( 0.23, 0.12). Based on that interval do we have evidence that there is a difference between the proportions of smokers in the two countries? (A)Yes (B) No (C) Not enough information to determine

5 Extra Credit Question (5 points ) Give a rough sketches of scatterplots that fit the descriptions, label both axis on each plot a)this scatterplot shows relatively strong, but not perfect negative linear trend between x and y. b) This scatterplot shows some relationship between x and y, but it is not a linear relationship.