T he population of male industrial workers in London who have never experienced

Question

The population of male industrial workers in London who have never experienced a major coronary event has mean systolic blood pressure 136 mm Hg (NO MEAN). You might be interested in determining whether those values are the same as those for the population of industrial workers who have suffered a coronary event. A sample of 35 workers who have experienced a major coronary event has mean systolic blood pressure of 143 mm Hg and sample standard deviation of 24.4 mm Hg. Researchers wish to see if those who have had a major coronary event have lower systolic blood pressures than those who have not

a. Perform an appropriate test at the 0.05 level of significance (i.e. one sample t test because is unknown)

b. Construct a 95% Confidence Interval for the true mean systolic blood pressure among those who have suffered a coronary event.

c. Based on the confidence interval above, what can you conclude? How does this relate to hypothesis testing?

Explanation / Answer

here null hypothesis: Ho:mean =136

alternate hypothesis: H1: mean <136

std error of mean =std deviation/(n)1/2 =24.4/(35)1/2 =4.124

hence test stat t=(X-mean)/std error =(143-136)/4.124=1.6974

for above test stat p value =0.9506

as p value is very high ; we can not reject null hypothesis.

There is insufficient evidence to conclude that those who have had a major coronary event have lower systolic blood pressures than those who have not.

b) for 95% CI and (35-1) =34 degree of freedom ; critical value of t =2.0322

therefore confidence interval =sample mean -/+ t*std error =134.62 ; 151.38

c)as our confidence interval contains values above 136 as well therefore

we can not reject null hypothesis.

There is insufficient evidence to conclude that those who have had a major coronary event have lower systolic blood pressures than those who have not.

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