Question

The tuft bind strength of a synthetic material used to make carpets is known to have a mean of 100 lb and standard deviation of 20 lb. A sample of 40 is randomly selected and the average strength was found as 105lb. Let μ denote the average tuft strength. Could it be that the average tuft strength is above 100 lb? Based on the information, what should be the appropriate null and alternative hypotheses for the purpose of your analysis?

Answer 1

The null hypothesis is:
`H_(0): \mu = 100`

The alternative hypothesis is:
`H_(a): \mu > 100`

Explanation:

At the null hypothesis, we test if the mean is equal to a certain value.

At the alternate hypothesis, we test if the mean is less than, more than, or different from the value tested at the null hypothesis.

The tuft bind strength of a synthetic material used to make carpets is known to have a mean of 100 lb and standard deviation of 20 lb.

This means that the null hypothesis is:
`H_(0): \mu = 100`

Could it be that the average tuft strength is above 100 lb?

The world above means that the appropriate alternative hypothesis is:
`H_(a): \mu > 100`