Question

A manufacturer of pharmaceutical products analyzes a specimen from each batch of a product to verify the concentration of the active ingredient. The chemical analysis is not perfectly precise, but the company wants to know the true mean concentration. The laboratory analyzes each specimen 40 times and reports the sample mean concentration to be 0.8404 and the sample standard deviation to be 0.0420.

1. The manager of the research team claims that the true mean concentration is 0.88. Based on the interval, is this true? Why?

2. If we had used a confidence level of 99%, would our confidence interval have been wider or narrower?

3. Suppose the researcher tested 30 samples instead of 40 but the mean and standard deviation was the same. Would our 95% confidence interval have been wider and narrower?

Answer 1