STAT 302 Practice Final Exam Solutions (Q28-Q50)

Quiz: Final - Practice Exam Question 28 2 pts Use the following information for questions 28-29: Suppose you conduct a hypothesis test to determine whether or not the average height of first-grade students is less than 46 inches. You conduct this test at the 0.05 significance level and come to the conclusion that 0.05 < p-value < 0.10. 28. What is the correct decision? o Accept the Null Hypothesis. o Accept the Alternative Hypothesis. O Reject the Null Hypothesis. � Fail to Reject the Null Hypothesis. p-value > 0.05 = alpha, we fail to reject the null Question 29 2 pts Use the following information for questions 28-29: Suppose you conduct a hypothesis test to determine whether or not the average height of first-grade students is less than 46 inches. You conduct this test at the 0.05 significance level and come to the conclusion that 0.05 < p-value < 0.10. 29. What is the appropriate conclusion? H0:mu = 46,HA:mu<46 we fail to reject the null, that means, data was rot .. ...J sufficiently in favor of HA a The data does not provide statistically significant evidence that the average height of first-grade students is less than 46 inches. o The data does provide statistically significant evidence that the average height of first-grade students is less than 46 inches. o The data does not provide statistically significant evidence that the average height of first-grade students is 46 inches. O The data does provide statistically significant evidence that the average height of first-grade students is 46 inches. Question 30 2 pts https://canvas.tamu .edu/courses/210724/quizzes/390987/take?preview = 1 14/33

Quiz: Final - Practice Exam Suppose a researcher wants to test the hypothesis that 1,1 = 25 versus the alternative that 1,1 #: 25 using data from a random sample of 95 people. We calculate the standardized test statistic to be 2.087. Which of the following best describes the p- value? O 0.05 < p-value < 0.04. 'SJ 0.04 < p-value < 0.05. o 0.02 < p-value < 0.04. O 0.02 < p-value < 0.025. O 0.01 < p-value < 0.02. Question 31 HO: mu = 25, HA: mu not equal to 25 n = 95, under the null, xbar ~ t (mu0 = 25, s/sqrt(n)), df = n-1 = 94 p-value = P(t94 >2.087)*2: between 0.04 and 0.05 Note. df 94 is not on t table. read df 80 instead (the next low r df) 2 pts Use the following information for questions 31-33: One treatment for strep throat is a tonsillectomy (having the tonsils removed). A research study wanted to determine wnetner or not having a tonsillectomy reduced the occurrence of strep throat in pediatric patients. They recruited 40 pediatric patients who had a tonsillectomy for their study and for each patient measured both the number of occurrences of strep throat in the year prior to the tonsillectomy (untreated) and the number of occurrences of strep throat in the year following the tonsillectomy (treated). The summary statistics for the study is shown in the table below (note: not all information in the table is required to solve the problem; you must decide what pieces of information are necessary). Assuming all conditions are met, conduct the appropriate hypothesis test at the 0.01 significance level to determine if patients have less cases of strep throat after treatment [difference = untreated (before tonsillectomy) - treated (after tonsillectomy)]. 1 G r oup "' i s � n t r e ated (Before TonSlfeclomy) �i 7 · t - � T reate d (After To n s i ll e c tom y } 40 2.3 4.9 Dinerence 1 40 4 . ' 9 1 3 .. 2 31. What are the hypotheses? paired t-test: two measurements are not independent (re eated measurements at pre- and post- treatment from the sam individuals) https://canvas.tamu .edu/courses/210724/quizzes/390987/take?preview = 1 15/33

Quiz: Final - Practice Exam 32. What is the value of the test statistic? xbar_diff = 4.9, s_diff = 3.2 SE = s_diff/sqrt(n) = 3.2/sqrt(40) ) df = n-1 = 39 0 1.5313 0 4.2933 0 8.5919 ?i 9.6838 0 13.6948 t = (xbar_diff - mu_0) / (s_diff/sqrt(n)) = (4.9-0)/(3.2/sqrt(40)) = 9. 838 Question 33 2 pts Use the following information for questions 31-33: One treatment for strep throat is a tonsillectomy (having the tonsils removed). A research study wanted to determine whether or not having a tonsillectomy reduced the occurrence of strep throat in pediatric patients. They recruited 40 pediatric patients who had a tonsillectomy for their study and for each patient measured both the number of occurrences of strep throat in the year prior to the tonsillectomy (untreated) and the number of occurrences of strep throat in the year following the tonsillectomy (treated). The summary statistics for the study is shown in the table below (note: not all information in the table is required to solve the problem; you must decide what pieces of information are necessary). Assuming all conditions are met, conduct the appropriate hypothesis test at the 0.01 significance level to determine if patients have less cases of strep throat after treatment [difference = untreated (before tonsillectomy) - treated (after tonsillectomy)]. 1 G r oup "' i s � n t r e ated (Before T o n S lf ecl om y ) �i 7 · t -3 T r e at ed (After T on s i l l e c tom y } 40 2.3 4.9 o·nerence 1 40 4. ' 9 1 3 .. 2 33. What is the following best describes the p-value? t = 9.6838, df = 39 Right tailed HT, thus p-value = P(t_39 > = 9.6838 ), df 39 is Flot located on t table, instead read the next lower df 30 : O p-value = 0 � p-value < 0.0005 P(t_30 > = 9.6838 ) <0.0005, since the cutoff t_30 for upper p 0.0005 is .646 https://canvas.tamu .edu/courses/210724/quizzes/390987/take?preview = 1 17/33

O p-v a lue < 0.001 O p-v a lue > 0.0005 O p-v a lue = 1 Question 34 Quiz: Final - Practice Exam 2 pts A recent study compared tooth health and periodontal damage in a group of 46 young aclult males wearing a tongue piercing ancl a control group of 46 young adult males inde pende without a tongue piercing. One question of interest was whether individuals with nt tvo tongue piercings had more enamel cracks on average. The summary statistics for th e8 arr p i es study are shown in the table below (note: not all information in the table is required to solve the problem; you must decide what pieces of information are necessary). Assuming all conditions are met, what is the 99.5% confidence interval for the difference between the number of enamel cracks in the two groups (difference = Tongue Piercing - No Tongue Piercing). 99.5% confidence level corresponds to 0.005 two sided prob Group n i s T o n g u e Piercing 46, 4. 0 1 3. 5 No T o n g ue , P i e rc i n g 46 , 1.2 1.3 Difference 46 2. 8 1 0.9 - Cl for two s a mple difference (mu1-mu2) = (xb a r1 - xb a r2) + - t*_df x SE, 0 (-4.4355, -1.1645) � .1645, 4.4355) 0 (1.2547, 4.3453) 0 (1.8401, 3.7599) 0 (2.4057, 3.1943) where SE = sqrt( s 1"2/n 1 + s2"2/s2 ) = sqrt( 3.5"2/46 + 1.3"2/41 ) = 0.55 xb a r1 - xb a r2 = 4.0-1.2 =2.8 Question 35 df = min(46-1, 46-1) = 45 (not on the t a ble, re a d df=40 inste a d) t*_ 40 = 2.971 99.5% Cl = 2.8+ - 2.971*0.55 = (2.8-1.6355, 2.8+1.6355) 2 pts We are testing the following hypotheses: https://canvas.tamu .edu/courses/210724/quizzes/390987/take?preview = 1 18/33

Quiz: Final - Practice Exam below). Assuming all conditions are met, conduct the appropriate hypothesis test using a significance level of 0.01. - Source DF Sum of Mean Square F Ratio Squares Antibiotic 8 k-1 449.33 224.67 5.207 Error n-k = 15 D E C. Tota , I C =n-1 1 0 9 6.50 37. What value belongs in blank space B? k=3, n=18, alpha=0.01 0 3 O 1 7 0 18 O Impossible to Determine Question 38 Use the following information for questions 37-40: -- Prob> F 0.0 1 92 2 pts Brock is interested in determining if 3 different antibiotics have different recovery times. He collected data on 6 patients taking each type of antibiotic (for a total of 18 patients) and ran the test using JMP software (partial results shown in the table below). Assuming all conditions are met, conduct the appropriate hypothesis test using a significance level of 0.01. Source Antibiotic Error C. Tota.I DF 8 C Sum of Squares Mean Square F Ratio SSG= 449.33 MSG= 224.67 15 D SSE SS T = 1 09 6 .5 0 E MSE 38. What value belongs in blank space E? https://canvas.tamu .edu/courses/210724/quizzes/390987/take?preview = 1 Prob> F 5.207 0.0 1 92 20/33

� 43.14 0 647.17 0 1545.83 0 103.06 O Impossible to Determine Question 39 Quiz: Final - Practice Exam SSE= SST-SSG=1096.5-449.33 MSE=SSE/15 or use F ratio: MSG/MSE= 5.207 --> MSE= 224.67/5.207 = 43.14 Use the following information for questions 37-40: 2 pts Brock is interested in determining if 3 different antibiotics have different recovery times. H e collected data on 6 patients taking each type of antibiotic (for a total of 18 patients) and ran the test using JMP software (partial results shown in the table below). Assuming all conditions are met, conduct the appropriate hypothesis test using a significance level of 0.01. - Source Antibiotic Error C. Tota.I DF 8 C Sum of Squares 449.33 15 D 1096.50 Mean Square F Ratio 224.67 E 39. What are the appropriate hypotheses? � : µAntibiotic 1 = µAntibiotic 2 = µAntibiotic 3 HA: �t least one mean recovery time is different. Prob> F 5.207 0.0192 0 Ho: P1 = P2 HA: P1 '# P2 mu1 not eq m2, or mu1 not eq m3, or mu2 not eq mu3 0 Ho: µd = 0 HA: µd '# 0 0 Ho: µAntibiotic 1 = µAntibiotic 2 = µAntibiotic 3 HA: µAntibiotic 1 '# µAntibiotic 2 '# µAntibiotic 3 https://canvas.tamu .edu/courses/210724/quizzes/390987/take?preview = 1 21/33

Quiz: Final - Practice Exam Question 41 2 pts A study of moisture and mold spores showed that in general, environments with a higher moisture content had increased number of mold spores. Moisture content explained 64% of the variation in the number of mold spores. What is the numerical value of the correlation between moisture content and mold spores? R A 2 =0.64 R = sign of association* sqrt(0.64) = (+1) 0.8 =0.8 0 -0.80 0 -0.64 0 0.4096 0 0.64 'g 0.80 the higher moisture content tends to increase mold spores (positive association) O Impossible to Determine Question 42 2 pts For a table of national information regarding a specific country, it is found that the correlation with Internet use is 0.545 for GDP, 0.734 for cellular-phone use, 0.664 for literacy, -0.893 for fertility, and 0.854 for CO2 emissions. Which variable has the weakest linear association with Internet use? see the absolute value: j0.545I is the smallest one � GDP has the weakest linear association with Internet use. O Cellular-phone use has the weakest linear association with Internet use. O CO2 emissions has the weakest linear association with Internet use. O Fertility has the weakest linear association with Internet use. O Literacy has the weakest linear association with Internet use. Question 43 https://canvas.tamu .edu/courses/210724/quizzes/390987 /take?preview = 1 2 pts 23/33

Quiz: Final - Practice Exam y x ( explanat ry variable) Given the regression output below for predicting the heart weight of cats from body weight, calculate the intercept. Note that the average body weight in the sample is 2.72 kg and the average heart weight is 10.63 grams. xbar Coefficients Bwt Estimate 4.0341 II b1 ,h .�P J-- Std. t value Error 0.2503 16.119 Pr(>ltl) >2e-16 0 -54.4 ?s/ -0.34 0 0.34 bO = ybar - xbar * b1 = 10.63-2.72*4.03 = 10.63-10.97 =-0.34 O 4.0341 0 9.62 O Impossible to Determine Question 44 Use the following information for questions 44-47: 2 pts Cathy wants to see if she can predict house prices based on square footage. She decides to use simple linear regression and gets the output shown below. Assuming all conditions are met, conduct the appropriate hypothesis test at the 5% level to determine if there is a positive linear relationship between square footage and house price. Regression Coeff. Standard Error I-value p-value Table Intercept 4 78 1. 93 0 7 1 62 85 .48 1 9 1 0 . 7 608 1 0.45 Square Footage 61.3667 3.6246 1 6.9306 0,0 0 10 44. What are the appropriate hypotheses? this is the p-value for two si ed test evaluating linear association such that HO: beta1 =O, HA: beta1 not eq 0 https://canvas.tamu .ed u/courses/21 0724/q uizzes/390987/take?preview = 1 24/33

0 0.01 0 0.05 0 0.10 0 0.5 0 5 Question 46 Quiz: Final - Practice Exam Use the following information for questions 44-47: 2 pts Cathy wants to see if she can predict house prices based on square footage. She decides to use simple linear regression and gets the output shown below. Assuming all conditions are met, conduct the appropriate hypothesis test at the 5% level to determine if there is a positive linear relationship between square footage and house price. Regression Coeff . Standard Error I - va l u e p-value Table Intercept 4 78 1. 93 0 7 1 62 8 5 .48 19 1 0. 7608 1 0 . 45 Square Footage 61.3667 3.6246 16.9306 0.0010 46. What is the p-value? rue model: Y = betaO + beta1 X + e p silon predicted model: yhat= 4781.9307 + 61.3667 X Test 'positive' association means: HO: beta1=O vs. HA: beta1 >O 0 0.0005 0 0.0010 0 0.225 0 0.45 p-value for one-sided test= p-value for two sided test= 0.0010/2 = 0.0005 Question 47 2 pts Use the following information for questions 44-47: https://canvas.tamu .ed u/courses/21 0724/q uizzes/390987/take?preview = 1 26/33

Quiz: Final - Practice Exam Cathy wants to see if she can predict house prices based on square footage. She decides to use simple linear regression and gets the output shown below. Assuming all conditions are met, conduct the appropriate hypothesis test at the 5% level to determine if there is a positive linear relationship between square footage and house price. Regression Coeff .. Standard Error t-value p-value Table Intercept 4781.9307 628 5 .4 8 1 9 1 0.7608 0.45 Square Footage 6 1 ' . 3667 3.6246 16.9306 0.0010 47. Cathy's house is 2034 square feet and costs $151,000. What is the residual for Cathy's house? 0 -129,601.80 0 -21,398.20 � , 398 .20 0 12 9 ,601. 8 0 O Impossible to Determine Question 48 rue model: Y = beta0 + beta1 X + epsilon predicted model: yhat= 4781.9307 + 61.3667 X predicted value for x=2034, yhat= 4781.9307 + 61.3667* 2034=129601.8 residual= y-yhat= 151000- 129601.8 = 21398.2 2 pts The scatterplot below shows the relationship between the percent of families that own their home and the percent of the population living in urban areas for each state. A residual plot is also shown. Based on the residual plot, what do you observe and what does that tell you about if a least-squares regression line is appropriate for this data? https://canvas.tamu .edu/courses/210724/quizzes/390987/take?preview = 1 27/33

Quiz: Final - Practice Exam Marco's mom has measured his height in centimeters every few months between the ages of 4.5 and 7.5. The recorded values are best estimated by the regression line with the equation y = 80.46 + 6.25x. Marco's mom wants to use this equation to predict if Marco will be taller than her when he is 14 years old. Doing this prediction is an example of what? O An influential point O Interpolation 14 is outside the ream of x range (4.5, 7 5) O Simple Linear Regression Hypothesis Test O Extrapolation --> prediction based on the fitted line is ot reliable (extrapolation) O A great idea! Question 50 2 pts The scatterplot below shows an outlier in the bottom left. What kind of outlier is this point? • laid horizontally awy from the center of group it changes the slope of re ression line O The point is both a high leverage point and an influential point. O The point is neither a high leverage point nor an influential point. O The point is a high leverage point, but not an influential point. O The point is not a high leverage point, but it is an influential point. 29/33