Question

government regulations restrict the amount of pollutants that can be released to the atmosphere through industrial smokestacks. to demonstrate that their smokestacks are releasing pollutants below the mandated limit of 7 parts per billion pollutants. rem industries collects a random sample of 24 readings. the mean pollutant level for the sample is 6.55 parts per billion with a population standard deviation of 0.9 parts per billion. do the data support the claim that the average pollutants produced by rem industries are below the mandated level at a 0.05 significance level? assume the population of readings is approximately normally distributed. step 2 of 3: compute the value of the test statistic. round your answer to two decimal places.

Explanation:

Step1: Identify the formula for z - test statistic

The formula for the z - test statistic in a one - sample z - test is $z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}$, where $\bar{x}$ is the sample mean, $\mu$ is the population mean, $\sigma$ is the population standard deviation, and $n$ is the sample size.

Step2: Identify the given values

We are given that $\bar{x} = 6.55$, $\mu=7$, $\sigma = 0.9$, and $n = 24$.

Step3: Substitute the values into the formula

$z=\frac{6.55 - 7}{\frac{0.9}{\sqrt{24}}}=\frac{- 0.45}{\frac{0.9}{\sqrt{24}}}=\frac{-0.45}{\frac{0.9}{4.899}}\approx\frac{-0.45}{0.184}\approx - 2.45$

Answer:

$-2.45$