Question

A hypothetical study concerned with estimating the amount of marijuana use per year among a teenage population obtained a sample of 125 high school students. The average number of times per year a student used marijuana was 4.7, with a standard deviation of 2.9. Construct a 99% confidence level, what is the LOWER bound for the confidence interval

Answer 1

Answer:

Confidence interval 99%

$4.0\leq\mu \leq 5.4$

Step-by-step explanation:

In this case, we have to estimate a confidence interval (CI) with an unknown standard deviation of the population (we only known the s.d. of the sample).

The estimated standard deviation is

$s_M=s/\sqrt{N}=2.9/\sqrt{125}=2.9/ 11.18=0.26$

For a 99% CI and degrees of freedom df=124, the t-statistic is t=2.616.

So the confidence interval is:

$M-t*s_M\leq \mu\leq M+t*s_M\\\\4.7-2.616*0.26\leq\mu \leq 4.7+2.616*0.26\\\\4.7-0.68\leq\mu \leq 4.7+0.68\\\\4.0\leq\mu \leq 5.4$