Question

There is some variability in the amount of phenobarbital in each capsule sold by a manufacturer. However, the manufacturer claims that the mean value is 20.0 mg. To test this, a sample of 25 pills yielded a sample mean of 19.7 with a sample standard deviation of 1.3. What inference would you draw from this data? In particular, is the data strong enough evidence to discredit the claim of the manufacturer? use the 5 percent level of significance.

Answer 1

To test the manufacturer's claim of a mean value of 20.0 mg for phenobarbital capsules, a hypothesis test can be performed using a t-test. If the test statistic falls outside the critical value range, the claim can be discredited.

Step-by-step explanation:

To test whether the manufacturer's claim of a mean value of 20.0 mg is accurate, we can perform a hypothesis test.

1. Null hypothesis (H0): The true mean is 20.0 mg.

2. Alternative hypothesis (H1): The true mean is not 20.0 mg.

3. Test statistic: We will use a t-test since the sample size is small (<30) and the population standard deviation is unknown.

4. Calculate the test statistic: t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))

5. Determine the critical value: For a 5% level of significance and 24 degrees of freedom (sample size - 1), the critical value is approximately ±2.064.

6. Compare the test statistic to the critical value: If the test statistic falls outside the critical value range, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.