A nighttime cold medicine’s label indicates the presence of 600 mg of acetaminophen in each fluid ounce of the drug. The FDA randomly selects 65 1-ounce samples and finds the mean content is 595 mg with a standard deviation of 20 mg. Is there evidence that the label is incorrect? Use a= .05.

And for this case since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mena is different from 600 mg

Step-by-step explanation:

Information given

[tex]\bar X=595[/tex] represent the sample mean

[tex]s=20[/tex] represent the sample standard deviation

[tex]n=65[/tex] sample size

[tex]\mu_o =600[/tex] represent the value to verify

[tex]\alpha=0.05[/tex] represent the significance level

t would represent the statistic

[tex]p_v[/tex] represent the p value

System of hypothesis

We want to test if the true mean is different from 600 mg, the system of hypothesis would be:

Null hypothesis:[tex]\mu = 600[/tex]

Alternative hypothesis:[tex]\mu \neq 600[/tex]

The statistic would be given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)

Replacing the info we got:

[tex]t=\frac{595-600}{\frac{20}{\sqrt{65}}}=-2.016[/tex]

The degrees of freedom are given by:

[tex]df=n-1=65-1=64[/tex]

The p value would be given by:

[tex]p_v =2*P(t_{(64)}<-2.016)=0.048[/tex]

And for this case since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mena is different from 600 mg