Assume that the weight of cereal in a "12.6 ounce box" is N(µ,0.42). The Food and Drug Association (FDA) allows only a small percentage of boxes to contain less than 12.6 ounces. You collect a random sample of n = 35 boxes and find that the sample mean is 12.8. Test the null hypothesis H0: µ = 13 against the alternative hypothesis HA: µ < 13 at level of significance α = 0.01

We reject the null hypothesis and accept the alternate hypothesis, that is, that the mean is less than 13 ounces.

Step-by-step explanation:

The null hypothesis is:

The alternate hypotesis is:

The test statistic is:

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

13 is tested at the null hypothesis:

This means that

N(µ,0.42)

This means that the standard deviation is 0.42, that is,

You collect a random sample of n = 35 boxes and find that the sample mean is 12.8.

This means that

Value of the test statistic:

Pvalue of the test:

The pvalue of the test is the pvalue of z = -2.82.

Looking at the z table, z = -2.82 has a pvalue of 0.0024

0.0024 < 0.01, which means that we reject the null hypothesis and accept the alternate hypothesis, that is, that the mean is less than 13 ounces.

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step-by-step explanation: