Question

A sanitation supervisor is interested in testing to see if the mean amount of garbage per bin is different from 50. In a random sample of 36 bins, the sample mean amount was 48.47 pounds and the sample standard deviation was 3.1 pounds. Conduct the appropriate hypothesis test using a 0.05 level of significance.\

Answer 1

Answer with explanation:

Given : Sample mean =$\overline{x}=\text{48.47 pounds}$

Standard deviation : $\sigma=\text{ 3.1 pounds.}$

Sample size : n = 36

Claim : $\mu\neq50$

∴ $H_0:\mu=50$

$H_1:\mu\neq50$

Since the alternative hypothesis is two tail , then the test is two tail test.

By using a z statistic and a 0.05 level of significance. Reject  $H_0$ if z < -1.960 or is z> 1.960.

Then , the test static for population mean is given by :-

$z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

$z=\dfrac{48.47-50}{\dfrac{3.1}{\sqrt{36}}}\approx-2.96$

We reject $H_0$ since $-2.96\leq -1.96$. We have statistically significant evidence at $\alpha=0.05$ to show that the mean amount of garbage per bin is not different from 50.