Solutions Practice Final Exam A Fall 2016 Multiple Choice Answers 1 a The output gives P value 0 0001 and is less than 0 05 We reject the null hypothesis The test is significant at 0 05 b is wrong because it was an observational study and we cannot establish cause and effect c is wrong because the chi square test is two sided where the alternative hypothesis only states there is an association and doesn t give a direction of more or less 2 a 3 c Test the slope of linear regression line for linear relationship of two quantitative variables Use one0 to test positively linear relationship sided alternative hypothesis e is wrong because is a notation used for estimated slope from sample data Hypotheses are statements about the population not sample 4 d Reasoning the statistical software output gives 2 sided P value for testing slope as a default Since the test statistic is 8 45 a positive value and the alternative hypothesis is HA 1 0 By the definition of P value you divide the P value of 0 0052 read in the Regression table by 2 5 c The definition of the slope statistic b1 is the estimated change in average response increase if slope 0 decrease if slope 0 for each increase in 1 of the explanatory variable value 6 a A very small P value provides strong evidence against the null hypothesis and hence support the alternative hypothesis However it cannot measure the strength of association 7 e 8 c Reasoning Statistical output tells us they are Comparing B A This implies the null hypotheses that software is calculating the p values for is H0 B A 0 With this order and the wheat farmer s hypotheses the hypotheses become H0 B A 0 vs HA B A 0 So the p value is the number next to Prob t Note that Calculation for relative risk p Truck p Car 2026 211581 2067 322584 1 50 There are 2 independent samples and it s a one sided test based on the description of the study 67 88 xA xB 76 70 so it makes sense that the p value is close to 1 9 c 10 b There are 4 possible outcomes i e four cells so the conditions require each expected count be 5 or larger 11 d With two very large independent samples the t score is very close to the z score Use the t Table and read the critical value z with corresponding one sided and two sided tail probabilities at the very bottom of the table Given 0 02 we can estimate the P value one sided P value 0 02 hence reject the H0 0 02 two sided P value 0 04 hence fail to reject H0 2 054 critical value z 2 326 corresponds to 2 tail probability 0 02 P value 0 04 Hence 2 22 could be the value of computed test statistic 1 12 a Based on the UT student s belief the hypotheses are H0 UT TAMU vs Ha UT TAMU You are told the two population means from census of all records TAMU 2 95 and UT 2 81 Since the p value 04 they will reject a true null hypothesis and make a Type I error The phrase the average GPR of UT students is statistically significantly greater is equivalent to saying the data provides statistical evidence the average UT GPR is greater 13 c 14 a Reasoning Note that P value is a conditional probability with the condition being given that Ho is true Hence the P value interpretation must always have at the statement something telling the reader that Ho is true So we must include the phrase 75 in the interpretation 15 Both d e are FALSE 16 d 17 b The null hypothesis states all the population means are the same hence no association By rejecting H0 the evidence supports the alternative hypothesis which states not all the population means are equal i e there is some association We should not make inference of which population mean is larger at this point We could only do so after performing pairwise multiple comparisons 18 b statement III is wrong because we don t usually randomly select subjects for experiments III would be a correct statement if experimental studies was replaced with observational studies 19 d Apply 2 proportion z test Be careful how you set up the alternative hypothesis where p1 and p2 represent the proportion of cyanobacteria in riparian and coastal populations respectively 20 d where Apply the formula 0 175 0 35 Review the BEAN regarding the power a is wrong because it if an inference about the sample mean and confidence intervals are inferences about population parameters b would be correct if the word sample was omitted c is wrong because again it has the sample mean in it Confidence interval statements are about the population parameter not the sample statistic 21 d a is wrong because the sample mean have nothing to do with margin of error The formula for the margin of error is t s n and this doesn t have x in it b is wrong because increasing the confidence level increases the margin of error because t is increased c is wrong because increasing the standard deviation causes s to increase 22 c The test was statistically significant because we rejected Ho but the effect size was only 21 on a scale of 0 10 So this is a very small increase for a course that costs 5000 2 23 a Reasoning There are two independent samples Use 2 sample t test because the response is numerical and the explanatory variable has 2 groups yes or no It isn t paired because there is no obvious pairing described Answer d is wrong because it is a statement about proportions but the response is numerical and with numerical responses we summarize the data using the mean not a proportion 24 b The is paired because the subjects plots of land were measured twice had cacti measured twice 25 a Read the three boxplots and find the computed difference for each pair has smaller standard deviation as it has smaller spread 26 c The power is solely a function of the sample size the true difference between the groups in the population the standard deviation and the significance level Since none of these change the power can t change The reason c is the answer is because 6 09 is further from 0 and so provides stronger evidence for Ha 27 d because the response variable outcome success of treatment Yes or No for each type of treatment Therefore data are summarized by proportions of success in each treatment group 28 b 29 a The left plot y versus x does not show a linear pattern so the response and the explanatory variables are not linearly related The right plot does not show an increase or decrease variations among the values of standardized residuals as the values of x increased So the SD s of y are pretty equal 30 c …