Question

In a study of store checkout-scanners it is claimed that 1% of sales are overcharged. (Before scanners were used, the overcharge rate was estimated to be about 1%)

a) State the hypotheses.

b) In general, what is a Type I error?

c) Describe what a Type I error is for this problem in words.

Answer 1

a) As we are testing here whether the proportion of overcharged sales is 1%, therefore the null and the alternative hypothesis here are given as:

H0: p = 1%

H1: p not equal to 1%

b) In general a type I error is given as the event where a true null hypothesis is rejected. Rejecting a true null hypothesis is called a type I error here.

c) Here, a type I error would mean given that the true proportion of overcharged sales is 1%, we conclude that the rue proportion of overcharged sales is not 1%. This is type I error here.