Question

A study is conducted to estimate blood pressure in people with glaucoma. In the study, 61 people with glaucoma are recruited. Mean systolic blood pressure is measured to be 140mmHg with a known standard deviation of 25mmHg. The researchers reported that the confidence interval for the true mean SBP among people with glaucoma is [134.651, 145.349].   

(a) What level of confidence did they use?

(b) Provide a practical interpretation of the confidence interval.

(c) Suppose that they wanted to test the null hypothesis H0: Mean SBP for people with glaucoma is 144. They want to use the confidence interval given above to make their decision.   

I. What is the significance level of the hypothesis test that corresponds to this confidence interval?

II. What decision should they make about the null hypothesis? Explain how you come to your conclusion.

Answer 1

Ans:

a)

df=61-1=60

critical t value=tinv(0.1,60)=1.671

90% confidence interval for mean

=140+/-1.671*(25/sqrt(61))

=140+/-5.349

=(134.651,145.349)

So,Level of confidence used=90%

b)We are 90% confident that true mean systolic blood pressure will fall between 134.651 and 145.349

c)

i)significance level=alpha=1-0.9=0.1

ii)As,144 is included within the limits of above CI,we fail to reject the null hypothesis.

There is not sufficient evidence to conclude that Mean SBP for people with glaucoma is different from 144.