Question

We want to investigate the average time per day students spend playing video games. We pick a simple random sample of 900 students and record how long they play video games per day. It turns out that the sample average is 2 hours and the SD of the sample is 1.25 hours.

Find the 91% confidence interval for our estimate of the average time per day spent playing video games.

Answer 1

Solution :

Given that,

Point estimate = sample mean =     = 2

Population standard deviation =     = 1.25

Sample size n =900

At 91% confidence level the z is ,

Z / 2   = Z0.045 = 1.70 ( Using z table )

Margin of error = E =   Z / 2     * ( /n)
= 1.70 * ( 1.25 / 900 )

= 0.0708
At 95% confidence interval estimate of the population mean
is,

- E <   < + E

2- 0.0708 <   <2 + 0.0708

1.9292 <   < 2.0708

(1.9292, 2.0708)