Question

A spice box manufacturing company is having difficulty filling packets to the required 50 grams. Suppose a business researcher randomly selects 60 boxes, weighs each of them and computes its mean. By chance, the researcher selects packets that have been filled adequately and that is how he gets the mean weight of 50 g, which falls in the "fail to reject" region.

The decision is to fail to reject the null hypothesis even though population mean is NOT actually 50 g.

Which kind of error has the researcher done in this case?

Answer 1

type II

Explanation:

got answer right in challenge 5.2

Answer 2

Answer: The researcher has made a Type II error in this case.

A Type II error occurs when the null hypothesis is not rejected even though it is false, i.e., the researcher fails to detect a significant difference when one actually exists. In this case, the null hypothesis is that the mean weight of the spice packets is 50 g, and the researcher has failed to reject this null hypothesis based on the sample mean of 50 g.

However, the population mean is not actually 50 g, and the researcher has made an error in failing to detect this difference. The sample size of 60 boxes may not have been large enough to detect a significant difference, or there may have been other factors that affected the measurements.

Therefore, the researcher has made a Type II error in this case by failing to reject the null hypothesis when it is actually false.

Explanation: