Final Practice Exam B Fall 2016 Solutions 1 b Reasoning Statement III isn t true because hypothesis tests are only designed to determine whether the data provides strong enough evidence for the HA that we can conclude it is true to a certain significance level 2 d 3 c Test the relationship between 2 categorical variables 4 c 5 b 22 is not a plausible population mean in the 90 CI and we would reject H0 at significance level 0 10 10 The P value must be less than 0 10 22 is a plausible population mean in the 95 CI and we would fail to reject H0 at significance level 0 05 5 The P value must be larger than 0 05 22 is a plausible population mean in the 99 CI and we would fail to reject H0 at significance level 0 01 1 The P value must be larger than significance level 0 01 Hence we conclude 0 05 P value 0 10 6 b Identify this is a one sample t test Compute the test statistic 2 use the t table with df 15 estimate the one sided P value 0 025 P value 0 05 Alternatively you could use calculator T Test and find the P value 0 03197 or compute tcdf 14 999 15 0 03197 7 e 8 a Because the study design is for 2 independent samples quantitative variable we use the t test output not the matched pairs output and the p value for which is Prob t 9 a c is wrong because it is a statement about only the subjects in the sample Based on the results of hypothesis tests we make inferences about the entire population not just the people who took part in the study The conclusion for a hypothesis test is always about a parameter and never about the sample 10 c 11 b 12 d The estimated average wholesale price is 3 50 2 50x but this equation is only good for x values between 20 and 50 see the scatterplot because this is the range of our explanatory variable values in the data set 13 a Identify this is a 2 independent samples t test assume unequal variance and apply the formula to compute the test statistic 0 78 or use calculator procedure 2 SampTTest 14 c 15 b They are pairing by year the man and woman were hired the same year salaries vary year by year so my pairing people hired the same year differences due to year are eliminated 16 b This is a randomized comparative experiment and the null hypothesis was rejected So the best conclusion is one which concludes some sort of causation rather than just association 1 17 a Because it asks for the relative risk of placebo gum compared to Xylitol gum we calculate relative risk as placebo Xylitol 49 178 1 70 29 179 18 a Reasoning The explanatory variable values from an Aggie family and Not from an Aggie family describe the groups whose proportions are being compared So the proportions of interest are pA and pNA These proportions must be proportion of successes maroon car in each group read similar arguments in 10 from the solutions for the 1st set of practice final exam 19 b The conditions are about the expected counts on the bottom row of each cell The expected cell count for the cell corresponds to From Aggie family and Has Maroon car is equal to 12 36 120 3 6 20 a Reasoning The explanatory variable consists of the treatment s being given to the patients In this case that is OC versus placebo The age of a subject isn t of interest but is just used for blocking purposes 21 b Reasoning The subjects are first divided up by age group The age groups form the blocks Then within each block the subjects are randomly divided up into treatment groups 22 a 23 a 24 b Compute the two sample proportions 45 60 0 75 40 50 0 8 and 0 0795 25 b Under the H0 p1 p2 which is equal to a common value of population proportion We shall pool all the sample data together to estimate this common population proportion For the SE of in the test statistic use the pooled sample proportion 0 7727 and 1 0 7727 0 2273 0 0802 26 d 27 e Statement I is wrong because sample mean is not part of the margin of error Statement II is wrong because decreasing the sample size increases the variability hence increases the size of margin of error Statement III is wrong because increasing the confidence level increases the size of the margin of error 28 b is not true c is true because the box plots don t overlap so there is statistical evidence the means differ at least when alpha is 05 or larger 29 c df1 k 1 df2 N k where k is the number of groups and N is the total sample size 2 30 b 31 d 32 b Hypotheses are about population parameters not sample statistics 33 e 34 c From the ANOVA table MSE pooled sample variance 35 e 3