Question

In a sample of

75

children, the mean age at which they first began to combine words was

16.27

months, with a standard deviation of

9.65

months.

Part 1 of 2

Construct a 99.8% interval for the mean age at which they first begin to combine words. Round the answers to two decimal places.

Answer 1

Solution :

Given that,

Point estimate = sample mean =     = 16.27

Population standard deviation =    = 9.65

Sample size n =75

At 99.8% confidence level the z is ,

= 1 - 99.8% = 1 - 0.998 = 0.002

/ 2 = 0.001

Z/2 = Z0.001 =3.09 ( Using z table )

Margin of error = E =   Z/2    * ( /n)
= 3.09 * ( 9.65 / 75 )

= 3.44
At 95% confidence interval estimate of the population mean
is,

- E < < + E

16.27 - 3.44 <   < 16.27 + 3.44

12.83<   < 19.71
(12.83,19.71 )