Question

A nurse in charge of Maternity Department of a hospital wants to estimate the mean time (in minutes) between a pregnant woman going into labor and delivery. The nurse measures delivery time of a random sample (n) of 25 women and finds a mean of 42 minutes with standard deviation of 6.1 minutes. Based on these findings, the nurse reports that the time of delivery of 90% of the cases would be between ___ and ___ minutes.

a. (30.0,40.2)

b. (39.9,44.1)

c. (35.6, 48.5)

d. (32.7,45.9)

Answer 1

Solution :

Given that,

= 42

s = 6.1

n = 25

Degrees of freedom = df = n - 1 = 25 - 1 = 24

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

t _/2,df = t_0.05,24 =1.711

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

= 1.711 * (6.1 / 25) = 2.1

The 90% confidence interval estimate of the population mean is,

- E < < + E

42 - 2.1 < < 42+ 2.1

39.9 < < 44.1

(39.9 ,  44.1 )