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For this assignment, use .05 for all inference. 1. White blood cell count (WBC) is measured on sample of 183 women. Some descriptive statistics, as well as a95% for the mean, are given below. Meam 7128.03 1724.37 i) We want to test fthe mean WBC differs from 7500. Complete the following steps (you'll use the edited printout below for some fthese). a) Write the null and alternative hypotheses. b) State the rejection region. c) Calculate the test statistic, to. d) State your decision to reject or fail to reject the null hypothesis. e) Interpret the result in the context of the problem. ii) Explain how you could use the CI above to reach the decision of the test part (i). iii) Suppose WBC not Normally distributed. Are you comfortable using the t-test in this setting, despite this? Why why not? 2. Using the "babies' data set from the lessons, we want to test the mean birth weight of female babies born to mothers who got poor prenatal care lessthan 3000 grams. i) Write the nul and alternative hypotheses. ii) The data were analyzed using PROC TTEST in SAS: edited results are below. State the test statistic and p-value, and interpret results in the context of the problem. Variable birthat = - Sad Dew Sad Err Minimura Maximum 435.8 92.7524 2043.0 3598.0 0.1349 3. This problem is related to Review Exercise p. 279 of the text but the numbers have changed. Cotinine levels (nmol/l) are measured hours and 24 hours after smoking ona sample of 12 people. We want to see the mean cotinine level differs for the two time periods. i) Are these paired or independent samples? Explain why you chose your answer. ii) Write the null and alternative hypotheses. Clearly explain any notation you use. iii) In the context of this problem, define what Type and Type errors are. iv) Edited results of test are given below. Interpret test results the context of the problem. Difference: cotminel2 ; Std Dev war Minimurn 5.9362 11.0000 28.0000 DE Pr>|t| 0.0003 4. Again using the "babies' data set from the lessons, we want to see mean length is smaller for female babies than for male babies, looking only at mothers who had good prenatal care. i) Are these paired or independent samples? Explain why you chose your answer ii) Write the null and alternative hypotheses. An edited portion of SAS printout is given below. Use this to answer parts (iii) (iv). Variable: length Mean Std Dev Sad Err Minimum Maximum de 20.3571 18.5000 24.0000 -0.6005 1.3674 0.2477 Variances 120 Unequal 119.96 -2.43 0.0083 Equality dr Varlances Num DF ii) When doing the test of interest, do you feel comfortable with the assumption of equal variances? Give some numeric justification for your answer. iv) Give the -value for the test of interest, and interpret results in the context of the problem. 5. We are planning study to compare mean reaction time between people with no alcohol consumption those who have had the equivalent of 24 ounces beer. We speculate that the mean reaction time will be 300 milliseconds theno alcohol group, and 360 milisecond group who had alcohol, and we therefore will doa one sided test. We also believe the standard deviation among participants within each group will be 60. i) Write the nul and alternative hypotheses being tested here. The code (provided i case you'r interested) needed to do power analysis is below, with corresponding edited printout on the next page. Use these to answer the following questions. ii) What sample size do we need to attain power of .6? iii) What sample size do we need to attain power of .9? iv) How would the answers to parts (ii) and (iii) change we changed the standard deviation from 60t 80? v) If recruiting each patient costs $150. how much would the study cost we want power of .8? Remember, the printout gives the sample size per group. vi) Rather than setting an priori power level like we did in parts (ii) (iv) suppose we want to use the results provided to decide on the sample size. State what sample size you would recommend, and justify why you chose this value. stddev Two Sample Test for Mean Difference 03 o

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