Question

Hypothesis test for M&Ms:

This section will work through constructing and interpreting a hypothesis test for

proportions. You can find the information for constructing a hypothesis test in

section 10.2. We will be using the p-value approach with a 5% significance level.

1. Treat your bag of M&M’s as a simple random sample. Choose your favorite

color of M&M’s you will be working with for this project. State the color

and give the counts below.

Color of choice: Green

The proportion of M&M's in your color: I had 12 green M&Ms in bag and total of M&Ms = 100... so 12/100?

The hypothesized proportion of M&M’s in your color:?

2. State the null and alternate hypothesis in both symbolic and sentence

form.

3. Use technology to find and state the p-value.

4. Based on your p-value and the significance given above, give the

conclusion of your hypothesis test.

Answer 1

1)

assuming p0 = 0.16 for green

The hypothesized proportion of M&M’s in your color: 0.16

(1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho p 0.16 0.16 Ha This corresponds to a two-tailed test, for which a z-test for one population proportion needs to be used (2) Rejection Region 0.05, and the critical value for a two- Based on the information provided, the significance level is a tailed test is ze = 1.96 The rejection region for this two-tailed test is R {z : \z| > 1.96} (3) Test Statistics The z-statistic is computed as follows: 0.12 0.16 -1.091 VPo (1 Po)T V0.16(1-0.16)/100 n (4) Decision about the null hypothesis Since it is observed that z 1.091 zc = 1.96, it is then concluded that the null hypothesis is not _ rejected. Using the P-value approach: The p-value is p 0.2752, and since p = 0.2752 > 0.05, it is concluded that the null hypothesis is not rejected. (5) Conclusion It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population proportion p is different than po, at the a 0.05 significance level.