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

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:

[tex]Z=\frac{(X-Xav)}{SD}[/tex]

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.