a) Is there evidence to support the claim that the test grouphas higher mean blo
ID: 2954273 • Letter: A
Question
a) Is there evidence to support the claim that the test grouphas higher mean blood pressure? Use =0.05, and assume thatboth populaitons are normally distributed but the variances are notequal. What is the P-value for this test? b)Calculate a confidence interval to answer the question inpart a). c)Do the data support the claim that the mean blood pressurefrom the test group is at least 15mmHg higher than the controlgroup? Make the same assumptions as in part a). d)Explain how the question in part c) could be answerdwith a confidence interval.Explanation / Answer
a) Is there evidence to support the claim that the test grouphas higher mean blood pressure? Use =0.05, and assume thatboth populaitons are normally distributed but the variances are notequal. What is the P-value for this test?The test hypothesis is
Ho:1>=2
Ha:1<2
=0.05, t(0.05, df=n1+n2-2=15) =1.75 (check student ttable)
The test statistic is
t=(xbar1-xbar2)/(s1^2/n1 + s2^2/n2)
=(90-115)/sqrt(5^2/8 + 10^2/9)
=-6.63
The p-value is P(t<-6.63) ˜0
Since p-value is less than =0.05, we reject Ho.
b)Calculate a confidence interval to answer the question inpart a).
(xbar1-xbar2) ±t*(s1^2/n1 + s2^2/n2)
--> (90-115)±1.75*sqrt(5^2/8 + 10^2/9)
--> (-31.6, -18.4)
c)Do the data support the claim that the mean blood pressurefrom the test group is at least 15mmHg higher than the controlgroup? Make the same assumptions as in part a).
The test hypothesis is
Ho:1-2> = -15
Ha:1-2<-15
The test statistic is
t=(xbar1-xbar2 +15)/(s1^2/n1 + s2^2/n2)
=(90-115+15)/sqrt(5^2/8 + 10^2/9)
= -2.65
Since t=-2.65<-1.75, we reject Ho. Therefore, the data supportsthe claim that the mean blood pressure from the test group is atleast 15mmHg higher than the control group.
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