Question

Suppose the supervisor of a warehouse has decided to select a random sample of 24 boxes of cherries from a particular grower’s crop and found the sample mean is 19.62 pounds with a standard deviation of weight from box to box is 0.5 pounds. He suspects the grower may be under-filling the boxes and is concerned with detecting this problem as the boxes are supposed to have 20 pounds. He is not concerned if the box contains more than 20 pounds.

a) Is the supervisor justified in concluding that under-filling of the boxes is occurring? Use the p-value method.

b) Determine the probability that a sample mean less than or equal to 19.62 pounds would be obtained from a sample of 24 boxes if the population mean was 20 pounds. What is the statistical term for the value you calculated?

Answer 1

We are given,

,   ,   

(a)

The Test statistics is given by

Now, assuming H₀ is true, the test statistics is

Now, the p-value is given by

As the p-value is less than 0.05, we have enough evidence to reject H₀.

Hence, we have enough evidence to conclude that under filling of boxes is occuring.

(b)  Now,

This is called P( Type I error)