Question

A researcher claims that the amounts of acetaminophen in a certain brand of cold tablets have a mean different from the 600mg claimed by the manufacturer. Test this claim at the 2% level of significance. The mean acetaminophen content for a random sample of n=48 tablets is 605mg. Assume that the population standard deviation is 4.8mg. Perform a hypothesis test for the population mean. Assume preliminary data indicate that it is reasonable to apply the z-test. Use the critical-value approach.

please show work, thank you.

Answer 1

Ans:

$H_0:\mu =600$

$H_a:\mu \neq 600$

Test statistic:

z=(605-600)/(4.8/sqrt(48))

z=7.22

critical z value=+/2.326

(rejection region:z<-2.326 or z>2.326)

As,test statistic falls in rejection region,we reject H₀.

There is sufficient evidence to support the claim that the amounts of acetaminophen in a certain brand of cold tablets have a mean different from the 600 mg