Question

A random sample of high school students are asked the number of hours they spent on social media. The hours are reported below:

3

5

6

7

8

10

12

13

14

15

You can assume the times are normally distributed with a standard deviation of 8.5.

a) Estimate with 90 percent confidence the mean number of hours spent on social media by all high school students. Show all working as part of your answer.

b) Interpret your findings in part a).

Answer 1

a) sample size,n=8

population standard deviation $\sigma=8.5$

sample mean $\overline{x}=\frac{3+5+6+7+8+10+12+13}{8}=64/8=8$

confidence level=90$\%$

significant level $\alpha=1-0.90=0.10$

the critical value for $\alpha=0.10, z_{\alpha /2}=1.645$

90% confidence interval$=\overline{x}\pm z_{\alpha/2}\times \sigma /\sqrt n=8\pm 1.645\times 8.5/\sqrt 8$

$=(8-4.9436,8+4.9436)=(3.0564,12.9436)$

b) based on the data provided the 90% confidence interval for the population mean is $(3.0564 \lt \mu \lt12.9436)$

we are 90% confident that the true population mean number of hours spent on social media by all high school students is contained in the interval (3.0564,12.9436)