The distribution of diastolic bloodpressures for the population of female diabet

Question

The distribution of diastolic bloodpressures for the population of female diabetics between the agesof 30 and 34 has an unknown mean and standard deviation. Asample of 10 diabetic women is selected; their mean diastolic bloodpressure is 84 mm Hg. We want to determine whether thediastolic blood pressure of female diabetics are different from thegeneral population of females in this age group, where the mean m =74.4 mmHg and standard deviation s = 9.1 mm Hg.

a) Conduct atwo-sided test at the = 0.05 level of significance todetermine whether diabetic women have a different mean diastolicblood pressure compared to the general population. Provide ap-value for the test.

b)      Would your conclusion have beendifferent if you had chosen = 0.01 instead of =0.05?

Explanation / Answer

n=10, X-bar=84, =74.4, =9.1 =0.05 (a)Ho:=74.4 Ha: not equal 74.4 The test statistics ist=(X-bar-)/(/n)=(84-74.4)/(9.1/10)=3.34 2*P-value=P(t(df=n-1=9) > 3.34)= 0.0087 Since the p-value is less than 0.025, reject Ho. (b) At =0.01, since p-value is large than 0.005, do notreject Ho.

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