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.

what is the original number? you forgot to add it.

to find the total number of combinations, multiply the quantity of each item by each other:

2 pairs of shoes x 3 pairs of shorts = 6 different combinations.