binf 702 spring 2014 practice problems practice problems binf 702 practice problems

BINF 702 Spring 2014 Practice Problems

Practice Problems

BINF 702 Practice Problems

Problem # 1



Problem # 1 Flow Chart Analysis Only one variable of interest? Yes One sample problem? No (Go to 1) Two-sample problem? Yes


Problem # 1 Flowchart Analysis Underlying distribution normal or can the

central-limit theorem be assumed to hold?? No Underlying distribution is

binomial? Yes Are samples independent? Yes

Problem # 1 Flowchart Analysis Are all expected values greater than or

equal to 5? Yes (go to 6) 2 x 2 contingency table? Yes (go to A) Use two-sample test for binomial

proportion, or 2 x 2 contingency table methods if no confounding is present, or the Mantel-Haenszel test if confounding is present.BINF 702 Spring 2014

Practice Problems

Problem #1 Solution



Problem # 1 Solution in R> prop.test(xx)

2-sample test for equality of proportions with continuity correction

data: xx X-squared = 5.6489, df = 1, p-value = 0.01747alternative hypothesis: two.sided 95 percent confidence interval: -0.38358985 -0.08699838 sample estimates: prop 1 prop 2 0.1000000 0.3352941

Problem # 2



Problem # 2 Flowchart Analysis Underlying distribution normal or can the central-limit

theorem be assumed to hold??

No Underlying distribution is

binomial? Yes Are samples independent? Yes

Problem # 2 Flowchart Analysis Are all expected values greater than or

equal to 5? Yes (go to 6) 2 x 2 contingency table? No (go to A) 2 x k contingency table?

Yes (go to B)



Problem # 2 Flowchart Analysis Interested in trend over k binomial

proportions? Yes

Use chi-square test for trend, if n confounding is present, or the mantel Extension test if confounding is present.

Problem # 2 Solution



Problem #2 in R> library(stats)> prop.trend.test(x = c(3,7,8,12), n = c(60,50,50,40))

Chi-squared Test for Trend in Proportions

data: c(3, 7, 8, 12) out of c(60, 50, 50, 40) ,

using scores: 1 2 3 4 X-squared = 10.9341, df = 1, p-value = 0.0009441


Problem # 3



central-limit theorem be assumed to hold?? Yes Inference concerning means? Yes (go to 3) Are samples independent? Yes


Problem # 3 Flowchart Analysis Are variances of two samples significantly

different? (Note – Should be tested using the F test)

No

Use two-sample t test with equal variances.


Problem # 3 Solution in R

> pt(q=8.94,df = 2198, lower.tail=FALSE)[1] 4.026324e-19


Problem # 4


Problem # 5a


Problem # 5b


Problem # 5c


Problem #5c in R

> 2 * pt(q=2.73, df = 19, lower.tail=FALSE)

[1] 0.01329876


Problem #6


Problem #6a

> 2 * pf(q=2.08, df1 = 24, df2 = 40,lower.tail=FALSE)[1] 0.03939543


Problem #6b



central-limit theorem be assumed to hold?? Yes Inference concerning means? Yes (go to 3) Are samples independent? Yes


Problem # 6 Flowchart Analysis Are variances of two samples significantly

different? (Note – Should be tested using the F test)

Yes

Use two-sample t test with unequal variances.

Problem #6c

Perform the test and report a p-value.> 2 * pt(q=5.34, df = 99,lower.tail=FALSE)[1] 5.929004e-07


Problem # 7



Problem # 7a


Problem # 7b


Problem # 7c

Which hypothesis test is appropriate here?


central-limit theorem be assumed to hold?? Yes Inference concerning means? Yes (go to 3) Are samples independent? No Use paired t test.



Problem # 7d

Conduct the hypothesis test and report a p-value.


Problem # 7d in Rx = c(142, 100, 112, 92, 104, 100, 108, 94, 104, 98)

y = c(154, 106, 110, 100, 112, 100, 120, 90, 104, 114)t.test(x=x, y = y, paired=TRUE) Paired t-test

data: x and y t = -2.6098, df = 9, p-value = 0.02828alternative hypothesis: true difference in means is not

equal to 0 95 percent confidence interval: -10.4541299 -0.7458701 sample estimates:mean of the differences -5.6

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