# M&M Project 4 Essay

Math 300

MM Project PT 4

August 14, 2011

Solution: We want to test the following null and alternative hypotheses

We need to use the z-statistic, which is calculated using

Observe that the sample proportion is

This corresponds to a two-tailed z-test for proportions. The z-statistics is computed by the following formula:

The critical value for for this two-tailed test is. The rejection region is given by

Since, then we reject the null hypothesis H0.

Hence, we have enough evidence to reject the claim that the true proportion of blue M&Ms® candies is 0.24.

3 pts. Test their claim that the true proportion of orange M&Ms® candies is 0.20 at the

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The critical value for for this two-tailed test is. The rejection region is given by

Since, then we fail to reject the null hypothesis H0.

Hence, we don't have enough evidence to reject the claim the true proportion of brown M&M’ss candies is 0.13.

3 pts. On average, they claim that a 1.69 oz bag will contain more than 54 candies. Test this claim (µ > 54) at the 0.01 significance (σ unknown). Solution: We are interested in testing the following null and alternative hypotheses

Considering that the population standard deviation is not given, we have to use a t-test using the following expression:

This corresponds to a right-tailed t-test. The t-statistics is given as follows:

The critical value for and for degrees of freedom for this right-tailed test is. The rejection region is given by

Since, then we reject the null hypothesis H0.

Therefore, we have enough evidence to support the claim that that a 1.69 oz bag will contain more than 54 candies.

BONUS: 5 pts. It is important that the total number of candies per bag does not vary very much. As a result of this quality control, the desired standard deviation is 1.5. Test the