Has the mean weight of courier packages dropped?

From extensive past records, µ = 18.3 kg and σ = 7.1 kg

Thirty packages in previous week had mean weight 16.8 kg

Use this diagram to illustrate how to find the p-value for testing µ when σ is a known value.

From the central limit theorem, the sample mean will have a normal distribution with standard devn σ / sqrt(n) and mean µ = 18.3 (assuming H0). This distn is shown in pale blue on the jittered dot plot of the data in the top left.

The sample mean is translated into a z-score on the right and the tail area from the standard normal distn is shown and translated into a p-value.

Since the p-value is quite large (0.124), there is no evidence that the mean weight of the packages has decreased.

Select Modified data from the pop-up menu and use the slider to discuss how different values for the sample mean would affect the conclusion.

A courier company suspects that the weight of recently shipped packages had dropped. From past records, the mean weight of packages was 18.3 kg and their standard deviation was 7.1 kg. These figures were based on a very large number of packages and can be considered as accurate.

Thirty packages were sampled from the previous week and their mean weight was found to be 16.8 kg.