Question

Pineapple Corporation (PC) maintains that their cans have always contained an average of 12 ounces of fruit. The production group believes that the mean weight has changed. They take a sample of 15 cans and find a sample mean of 12.05 ounces and a sample standard deviation of .08 ounces. What conclusion can we make from the appropriate hypothesis test at the .01 level of significance

Answer 1

We accept the null hypothesis, that is, that the mean weight of the cans is still of 12 ounces of fruit.

Explanation:

Pineapple Corporation (PC) maintains that their cans have always contained an average of 12 ounces of fruit.

This means that the null hypothesis is:
`H_0: \mu = 12`

The production group believes that the mean weight has changed.

This means that the alternate hypothesis is:

`H_a: \mu \\eq 12`

The test statistic is:

`z = (X - \mu)/((\sigma)/(√(n)))`

In which X is the sample mean,
`\mu` is the value tested at the null hypothesis,
`\sigma` is the standard deviation and n is the size of the sample.

12 is tested at the null hypothesis:

This means that
`\mu = 12`

They take a sample of 15 cans and find a sample mean of 12.05 ounces and a sample standard deviation of .08 ounces.

This means, respectibely, that
`n = 15, X = 12.05, \sigma = 0.08`

Value of the test statistic:

`z = (X - \mu)/((\sigma)/(√(n)))`

`z = (12.05 - 12)/((0.08)/(√(15)))`

`z = 2.42`

Pvalue of the test:

We are testing if the mean is different from a value, which means that the pvalue is 2 multiplied by 1 subtracted by the pvalue of z = 2.42.

Looking at the z-table, z = 2.42 has a pvalue of 0.9922

1 - 0.9922 = 0.0078

2*0.0078 = 0.0156

What conclusion can we make from the appropriate hypothesis test at the .01 level of significance?

0.0156 > 0.01. This means that at the 0.01 level, we accept the null hypothesis, that is, that the mean weight of the cans is still of 12 ounces of fruit.