Question

A bottling company wants to be sure that their 500 mL bottles of hydrating drink are being filled appropriately. They are mostly concerned if too much of the drink is in the bottles. A random sample of bottles filled by the drink are chosen and the amount of liquid in each bottle is measured.

a) State the null and alternative hypotheses. Write '≤' as '<=', '≥' as '>=', and '≠' as '<>'.

b) In context, explain what the Type I error is.

c) In context, explain what the Type II error is.

d) Which is worse for the bottling company, a Type I error or a Type II error? Why?

e) Which is worse for the consumer, a Type I error or a Type II error? Why?

Answer 1

a)

Here we need to test whether the hydrating drink is more than 500ml in the bottle, and as we know the null hypothesis is hypothesis with no difference the hypothesis would be as follows

Let mu denote the mean hydrating drink in the bottles

Ho: mu=500

Ha: mu > 500

b) Type 1 error is basically rejecting the null hypothesis given it is true so in this case it would be accepting that the hydrating drink in the bottle is more than 500ml but infact it is not greater than 500ml.

c) Type 2 error occurs when null hypothesis is accepted even though it is false so in this case it would be accepted that the mean is 500ml but infact it is greater than 500 ml.

d) Type 2 error is worse for the bottling company because type 2 error shows that the mean is 500ml but infact it is greater than 500ml so the company without realising would be in loss because the drink is filled assuming to be 500ml but it is greater than 500ml.

e) type 1 error is worse for the consumer because the consumer might be thinking that the hydrating drink is more than 500ml but infact it is not more than 500ml so the consumer would be getting the less quantity even though he must be thinking he is getting more of it.

Do comment if you have any doubt.

Thank you !!!