Question

A pediatrician asked a random sample of parents to report how long it took their toddler to fall asleep at night. Among 51 toddlers the mean time to fall asleep at night was 23.4 minutes with a standard deviation of 6.7 minutes. Fill in the missing values (rounded to one digit after the decimal point) to estimate the parameter.

Using 95% confidence, the mean time to fall asleep among all toddlers is between ______ and ______.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 23.4

sample standard deviation = s = 6.7

sample size = n = 51

Degrees of freedom = df = n - 1 = 51 - 1 = 50

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,50 = 2.009

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

= 2.009 * ( 6.7/ 51)

= 1.9

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

- E < < + E

23.4 - 1.9 < < 23.4 + 1.9

21.5 < < 25.3

A 95% confidence, the mean time to fall asleep among all toddlers is between 21.5 and 25.3