Question

A health care professional wants to determine whether individuals with hypertension who take Atenolol have significantly lower systolic blood pressure than individuals with hypertension who do not take Atenolol. For individuals who have not been prescribed Atenolol, the population systolic blood pressure mean is 165 (µ = 165). The 30 individuals who take Atenolol have an average systolic blood pressure of 180, with a sample standard deviation of 6. On the basis of these data, can the researcher conclude that the Atenolol significantly lowers systolic blood pressure?

Calculate the 95% confidence interval

The mean you will use for this calculation is:

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 180

sample standard deviation = s = 6

sample size = n = 30

Degrees of freedom = df = n - 1 = 29

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,24 = 2.045

Margin of error = E = t_/2,df * (s /n)

= 2.045* (6 / 30)

= 2.240

The 95% confidence interval estimate of the population mean is,

- E < < + E

180 - 2.240 < < 180 + 2.240

177.760 < < 182.240

(177.760 , 182.240)

The mean you will use for this calculation is: 180.