Question

A manufacturer is interested in determining whether it can claim that the boxes of detergent it sells contain, on average, more than 500 grams of detergent. The firm selects a random sample of 100 boxes and records the amount of detergent (in grams) in each box. The data are provided in the file P09_02.xlsx.


a.Identify the null and alternative hypotheses for this situation.

b.Is there statistical support for the manufacturers claim

Answer 1

Answer:

a) H0=Weight of detergent=500gr  (null hypotheses )

H1=Weight of detergent>500 gr. (alternative hypotheses )

b) X test.

Step-by-step explanation:

a)

The statement from which we are going to establish the assumptions is that supplied by the manufacturer, which says that the average weight of the detergent is 500 g. So:

H0=Weight of detergent=500gr  (null hypotheses )

H1=Weight of detergent>500 gr. (alternative hypotheses )

b)

You are not providing the source you mention where the sample of detergent boxes taken is located. So I will explain in general terms how the problem should be posed.

For this case, we can use Z test because the sample we are taking is larger than 30.

The first thing we have to do is calculate Z, which is given by:

$Z=\frac{(X-Xav)}{SD}$

Where:

Xav=Average of x.

SD=Standard deviation.

Then, we look for the table and if the value we have just calculated is greater than that of the table, then we must reject the null hypothesis.