Question

Abuse of substances containing toluene can produce various neurological symptoms. In an investigation of the mechanism of these toxic effects, researchers measured the concentrations of various chemicals in the brain of rats that had been exposed to a toluene-laden atmosphere, and also in unexposed control rats. The scientists want to ask if Toluene has any effect on the norepinephrine (NE) concentration in the brain (either increasing or decreasing the concentration). To summarize the data, the subtract the Control group average from the Toluene group average. The concentrations and summaries of the brain chemical norepinephrine (NE) in the medulla region of the brain are given:

543 523 431 635 564 580 600 610 550
Does the exposure to toluene significantly increase norepinephrine levels in rat medullas above the
normal median level of 530 ng/gm?

Answer 1

Yes. There is enough evidence, at a significance level of 0.05, to support the claim that the exposure to toluene significantly increase norepinephrine levels in rat medullas above the normal median level of 530 ng/gm.

Explanation:

This is a hypothesis test for the population mean.

The claim is that the exposure to toluene significantly increase norepinephrine levels in rat medullas above the normal median level of 530 ng/gm.

Then, the null and alternative hypothesis are:

`H_0: \mu=350\\\\H_a:\mu> 350`

The significance level is assumed to be 0.05.

The sample data is [543 523 431 635 564 580 600 610 550]. The sample size is n=9, the sample mean is M=559.556 and the sample standard deviation is s=59.727.

The estimated standard error of the mean is computed using the formula:

`s_M=(s)/(√(n))=(59.727)/(√(9))=19.909`

Then, we can calculate the t-statistic as:

`t=(M-\mu)/(s/√(n))=(559.556-350)/(19.909)=(209.556)/(19.909)=10.526`

The degrees of freedom for this sample size are:

`df=n-1=9-1=8`

This test is a right-tailed test, with 8 degrees of freedom and t=10.526, so the P-value for this test is calculated as (using a t-table):

`P-value=P(t>10.526)=0`

As the P-value (0) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the exposure to toluene significantly increase norepinephrine levels in rat medullas above the normal median level of 530 ng/gm.