STAT 5817, Exam I.Name:

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  1. In a study that examines the efficacy of saliva cotinine as an indicator for exposure to tobacco smoke. Six non-heavy smokers were in the study and all had abstained from smoking for at least one week prior to the study. Each of them is then required to smoke a single cigarette. Samples of saliva were taken from all individuals 12 and 24 hours after smoking the cigarette. The data collected is in the following table:

Cotinine Levels (nmol/L)
Subject / 1 / 2 / 3 / 4 / 5 / 6

After 12 hrs

/ 65 / 54 / 75 / 122 / 87 / 56

After 24 hrs

/ 54 / 24 / 63 / 87 / 66 / 42

It is believed that there is a difference between “the cotinine level 12 hours after smoking the cigarette” and “the cotinine level 24 hours after smoking”.

a)Find the 95% confidence interval estimate for average cotinine level after 24 hours.

b)At 0.05 level of significance, test to see if there is a significance difference between “the cotinine level 12 hours after smoking the cigarette” and “the cotinine level 24 hours after smoking”.

(Attach tables and charts to explain your results.)

  1. Periodically, the Mahoning County Water Department tests the drinking water of homeowners for contaminants such as lead and copper. The lead levels in water specimens collected in 2002 for a sample of 7 residents of the Boardman Township and a sample of 7 residents from the Canfield Township are shown below.

Lead level (g/L)
Boardman / 2.11 / 5.30 / .98 / 0 / 4.5 / 7.2 / 3.4
Canfield / 1.23 / .67 / 2.12 / .12 / 0 / 0 / 4.2

Perform a statistical significance test, at .05 level, to see whether there is a significant difference in average lead levels between the two townships. (Attach tables and charts that you think is necessary to explain your results. You need to at least show a table of descriptive statistics, SPSS normality test table if normality test is performed, a chart describing the data that is useful for checking the hypothesis and a SPSS hypothesis test table.)

  1. In a study of HIV infection among women entering the New York State prison system, hundreds of inmates were cross-classified with respect to HIV seropositivity and their histories of intravenous drug use. These data are stored in a data set prison.sav. The indicators of seropositivity are saved under the variable name hiv and those of intravenous drug use under indu.

a)What percentage of the inmates are HIV seropositive? (Use 95% confidence interval)

b)Among women who have used drugs intravenously, what proportion are HIV positive? Among women who have not used drugs intravenously, what proportion are HIV-positive? (Use 95% confidence interval to answer these questions.)

c)At 0.05 level of significance, test the null hypothesis that there is no association between history of intravenous drug use and HIV seropositivity. (Attach SPSS contingency table and significance test table.)