22S 30 105 Statistical Methods and Computing PRACTICE PROBLEMS for MIDTERM 2 Spring 2005 Instructor Cowles Midterm 2 14 15 16 17 18 Show your work on any problems that involve calculations There are 26 total points on this midterm Point values for each question are shown in parentheses I will grade on a curve and will give partial credit wherever possible Name Course no 30 or 105 1 3 You wish to estimate the population mean IQ test score of seventh grade girls in the Iowa City Coralville school district Suppose that the standard deviation of IQ scores in this population is known to be 15 points How large a sample of seventh grade girls would you need to estimate the population mean IQ score within 5 points with 90 confidence 100 125 114 95 117 We wish to use these data to test the null hypothesis that in the population of all insulin dependent diabetics the mean percentage of ideal body weight is 100 We do not know in advance whether to expect the population mean to be larger or smaller than 100 a 2 Write the null and alternative hypotheses using conventional symbols b 1 This is a circle one i ii iii iv one sided test two sided test Chi square test none of the above c 1 This study is set up as a circle one 2 Percentages of ideal body weight were determined for 18 randomly selected insulindependent diabetics A percentage of 120 means that an individual weighs 20 more than his or her ideal body weight while a percentage of 100 means that an individual weighs exactly his or her ideal body weight Data from Pagano and Gauvreau Principles of Biostatistics 2nd edition p 229 Here is a listing of the data Obs bwgtpct 1 2 3 4 5 6 7 8 9 10 11 12 13 107 119 99 114 120 104 88 114 124 116 101 121 152 1 i ii iii iv v one sample problem paired sample problem two idependent sample problem impossible to tell from the description given none of the above d 1 We wish to conduct our hypothesis test at significance level 01 This means that circle one i ii iii iv v We wish to have only We wish to have only We wish to have only We wish to have only None of the above a a a a 01 01 01 01 chance chance chance chance 2 of of of of failing to reject H 0 if H0 is false rejecting H 0 if H0 is false failing to reject H 0 if H0 is true rejecting H 0 if H0 is true e 1 The data is used to compute a 99 t confidence interval The SAS output is a 1 Will large values of x or small values of x enable him to reject H 0 large small Analysis Variable bwgtpct Lower 99 Upper 99 N Mean Std Dev CL for Mean CL for Mean 18 112 7777778 14 4244709 102 9241407 122 6314149 What quantity are we 99 confident lies in the interval 102 92 122 63 circle one i The sample mean of percent of ideal body weight from the 18 diabetics in the study ii The population mean of percent of ideal body weight in all insulin dependent diabetics iii The mean difference between ideal body weight and actual body weight iv None of the above f 2 Based on the confidence interval the correct decision regarding the hypothesis test is circle one i reject H0 at the 01 significance level ii fail to reject H0 at the 01 significance level iii impossible to draw a conclusion from the confidence interval iv none of the above g 2 Write one assumption required for the use of t tests and t confidence intervals h 2 What would you do to verify whether the assumption you listed in the previous question is met for this problem b 3 What is the sampling distribution of x if the null hypothesis is true Give the following the name of the distribution the mean numeric value the standard deviation numeric value c 3 The researcher chooses to conduct his hypothesis test at significance level 05 What is the cut off value of x that would enable him to reject H 0 Give a numeric answer Show your calculations d 3 What is the power of the test against the alternative 77 Give a numeric answer Show your calculations 3 A researcher wishes to investigate whether the mean resting heart rate in the population of undergraduate students at UI is greater than 75 beats per minute He states the hypotheses for his statistical test as H0 75 HA 75 He is convinced that resting heart rates in the population follow an approximately normal distribution with known standard deviation 8 He measures the resting heart rate on a simple random sample of 25 UI undergrads 3 4 e 1 Power in a statistical test is circle one i ii iii iv v The probability of rejecting H0 given that H0 is true The probability of rejecting H0 given that H0 is false The probability of failing to reject H 0 given that H0 is true The probability of failing to reject H 0 given that H0 is false None of the above 5
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