Question

A generic brand of the anti-histamine Diphenhydramine markets a capsule with a 50 milligram dose. The manufacturer is worried that the machine that fills the capsules has come out of calibration and is no longer creating capsules with the appropriate dosage.

Does the data suggest that the population mean dosage of this brand is different than 50 mg?

Answer 1

To determine if the population mean dosage of the generic brand of the anti-histamine Diphenhydramine is different than 50 mg, a hypothesis test can be conducted. The null hypothesis is that the population mean dosage is equal to 50 mg, and the alternative hypothesis is that the population mean dosage is different than 50 mg.

Step-by-step explanation:

To determine if the population mean dosage of the generic brand of the anti-histamine Diphenhydramine is different than 50 mg, a hypothesis test can be conducted.

First, the null hypothesis (H0) is that the population mean dosage is equal to 50 mg, and the alternative hypothesis (Ha) is that the population mean dosage is different than 50 mg. The next step is to collect a sample of capsules and measure their dosages.

Using statistical analysis, the sample mean dosage can be calculated and compared to the hypothesized value of 50 mg. If the sample mean is significantly different from 50 mg, then there is evidence to suggest that the population mean dosage of the brand is different than 50 mg. The significance level, denoted as alpha, determines the threshold for statistical significance.

For example, if alpha is set at 0.05, then the calculated p-value should be less than 0.05 to reject the null hypothesis and conclude that the population mean dosage is different than 50 mg.