Question

a manufacturer claims that a certain brand of cold tablets contains an average 600 mg of acetaminophen. to test this claim, a researcher creates a random sample of 36 tablets. the mean of this sample is 576.4 mg, and the standard deviation is 76.7 mg. test the claim using a level of significance of 10%.
a. calculate your p - value. write the result below and be sure to round your final answer to four decimal places.
b. the p - value is...
less than (or equal to)
greater than
c. do you reject the null hypothesis?
reject the null hypothesis
fail to reject the null hypothesis
accept the null hypothesis
d. what is the correct interpretation of this decision? using a 10% level of significance, there select an answer is not sufficient evidence to select an answer support reject accept the claim that a certain brand of cold tablets contains an average 600 mg of acetaminophen.

Explanation:

Step1: State the hypotheses

The null hypothesis $H_0:\mu = 600$ and the alternative hypothesis $H_1:\mu
eq600$. The sample size $n = 36$, sample mean $\bar{x}=576.4$, sample standard - deviation $s = 76.7$.

Step2: Calculate the test - statistic

The test - statistic for a one - sample t - test is $t=\frac{\bar{x}-\mu}{\frac{s}{\sqrt{n}}}$. Substitute the values: $\mu = 600$, $\bar{x}=576.4$, $s = 76.7$, and $n = 36$.
$t=\frac{576.4 - 600}{\frac{76.7}{\sqrt{36}}}=\frac{- 23.6}{\frac{76.7}{6}}=\frac{-23.6}{12.7833}\approx - 1.846$.

Step3: Determine the degrees of freedom

The degrees of freedom $df=n - 1=36 - 1 = 35$.

Step4: Calculate the p - value

Since this is a two - tailed test, the p - value is $2P(t_{35}\lt| - 1.846|)$. Using a t - distribution table or a calculator (e.g., in R: 2*pt(-1.846,35)), we find that the p - value is approximately $0.0728$.

Step5: Compare the p - value with the significance level

The significance level $\alpha = 0.10$. Since $0.0728\lt0.10$, we reject the null hypothesis.

Answer:

a. $0.0728$
b. less than (or equal to)
c. reject the null hypothesis
d. Using a 10% level of significance, there is sufficient evidence to reject the claim that a certain brand of cold tablets contains an average 600 mg of acetaminophen.