Practice Final Exam B 1 Which of the following statements are true about hypothesis tests I II We always assume the null hypothesis is true when the P value is calculated Then the data supports the alternative hypothesis the further the value of the test statistic from 0 then the stronger the evidence is in favor of the alternative hypothesis III Hypothesis tests are designed to determine probability that the null hypothesis is true or false a b c d e I only is true I and II only are true II only is true II and III only are true I I and III are all true 2 Suppose you are planning an experiment in which you are going to select a random sample of 236 cars and measure their CO2 emission levels As part of your report you decide to give a 95 confidence interval for average emission level If instead you report a 99 confidence interval what would be the impact on your estimation of the parameter I II III a b c d e You would decrease the range of plausible values for in your report if you report a 99 confidence interval rather than a 95 confidence interval The chance you will select a sample whose calculated confidence interval would not contain the true value of the mean would decrease from 5 to 1 You increase the chance that would be a value in the confidence interval I only is true II only is true I and II only are true II and III only are true All are true 3 A public health investigator claims there is an association between drinking habits and marital status of people in their thirties To answer her question she takes a SRS of 200 people in their thirties and asks them if they drink 1 or fewer drinks per day or 2 or more drinks per day She also asks them if they are married divorced or have never been married What would be the most appropriate choice for analyzing the resulting data a b c d e Independent 2 samples t test Paired t test Chi square 2 way table test Linear regression No test we ve studied this semester can be used to analyze this data set 1 4 Simpson s Paradox occurs when a no baseline risk is given so it is not known whether or not a high relative risk has practical importance b a confounding variable rather than the explanatory variable is responsible for a change in the response variable c the direction of the relationship between two variables changes when the categories of a confounding variable are taken into account d the results of a test are statistically significant but are really due to chance e we make statistical inferences about population 5 Data was collected to test a population mean with the hypotheses H0 22 versus HA 22 From this same data the following confidence intervals for were also calculated 90 confidence interval for 22 15 25 45 95 confidence interval for 21 84 25 76 99 confidence interval for 21 22 26 38 What can we conclude about the P value for testing the hypotheses H0 22 vs HA 22 a b c d e P value 0 10 0 05 p value 0 10 0 01 p value 0 05 p value 0 01 We need a test statistic to determine the p value in this case 6 The physician recommended dosage of a new medication is 14 mg Actual administered doses vary slightly from dose to dose and are normally distributed with mean A representative of a medical review board wishes to see if there is any evidence that the mean dosage is more than recommended and so intends to test the following hypotheses 14 against 14 To do this the physician selects 16 doses at random and determines the weight of each The physician finds the sample mean to be 14 12 mg and the sample standard deviation to be s 0 24 mg Based on these data a b c d e we would reject H0 at significance level 0 10 but not at 0 05 we would reject H0 at significance level 0 05 but not at 0 025 we would reject H0 at significance level 0 025 but not at 0 01 we would reject H0 at significance level 0 01 we would fail to reject H0 at significance level 0 10 7 For a regression model the standard error involved in estimating the population mean response of y at a particular value of x is the standard error involved in predicting an individual value of y at that same particular value of x a b c d e equal to greater than or equal to less than or equal to greater than less than 2 Sixteen patients with high blood pressure are randomly assigned to one of two groups In the first group just before their blood pressure was taken doctors asked the patients questions about their medical history and sources of stress in their lives In the second group just before their blood pressure was taken patients were asked to count to 400 Scientists want to test the theory the average blood pressure of patients who ve just talked to a doctor is different from the average blood pressure of patients who ve just counted but not talked to a doctor Assume all conditions are met Use this scenario and the output given below to answer the next 2 questions Level Counting Talking Number 8 8 Mean Std Dev 103 9 3 8 106 7 3 9 t Test Talking Counting Assuming unequal variances Difference 2 85 t Ratio Std Err Dif 1 89 DF Upper CL Dif 6 90 Prob t Lower CL Dif 1 20 Prob t Confidence 0 95 Prob t Matched Pairs Difference Talking Counting Talking 106 725 Counting 104 125 Mean Difference Std Error Upper 95 Lower 95 N Correlation 8 t Ratio DF Prob t Prob t Prob t 2 799586 7 0 0265 0 0133 0 9867 What is the correct P value to use to test the claim of the researchers a 0 1543 9 2 6 0 92871 4 79605 0 40395 8 0 73789 1 506309 13 95487 0 1543 0 0771 0 9229 b 0 0771 c 0 9229 d 0 0265 e 0 0133 What is the conclusion when the significance level is 0 01 a b c d e The data does not provide statistical evidence at the 01 significance level that the average blood pressure after talking to a doctor is different from the average BP after counting to 400 The data provides evidence at the 01 significance level that the average blood pressure after people talk to a doctor is higher than after counting to 400 The data does not provide statistical evidence at the 01 significance level that the average blood pressure of the 8 subjects talking to a doctor is different from the average BP of the 8 subjects who counted to 400 The data does not provide statistical evidence at the 01 significance level …