Question

Suppose we know that the average heart rate measured for the 30 days is 129.5 bps. Assume that fetal heart rate is normally distributed. He decides to use the sample’s Standard deviation of 12 bps because the populations Standard deviation is not known. Will this 95% confidence interval be more accurate than the confidence interval from above? Justify your answer.  

Answer 1

Solution :

Given that,

= 129.5

s = 12

n = 30

Degrees of freedom = df = n - 1 = 30 - 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 = t0.025,29=2.245

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

= 2.245* (12/ 30)

= 4.5

Margin of error = 4.5

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

- E < < + E

129.5 - 4.5< < 129.5 + 4.5

125.0 < < 134.0

(125.0, 134.0)