Constructing a Confidence Interval with M&Ms

1. a. Obtain a bag of plain M&Ms of size 1.69 oz (47.9 g). Treat your bag of plain M&Ms as a simple random sample.

b. Count the number of orange M&Ms and the total number of M&Ms in your bag. Then determine the proportion of your M&Ms that are orange.

The number or orange M&Ms is: _____________.

Then number of M&Ms in the bag is _____________.

The proportion of orange M&Ms is ____________.

c.Show that the requirements for constructing a confidence interval for the proportion are satisfied or are not satisfied. You will find the requirements for constructing the confidence interval for the population proportion in your text on page 427. these are

• All possible samples of a given size have an equal probability of being chosen; that is a simple random sample is used.
• The conditions for a binomial distribution are met.
• The sample size is large enough to ensure that np>10 and n(1-p)>10

Step 2. If the conditions are not met, what should you do?

d. Some credible sources suggest a different requirement for constructing a confidence interval when very little is a stake.These sources would say that a necessary and sufficient condition for this LAB would be if np > 5 and also n(1 - p) > 5 then the condition of normality is met. Show that your pack of M&Ms either does or does not meet this suggested normality condition.

2.Construct a 95% confidence interval for the proportion of orange M&Ms.After you have constructed the interval interpret the interval.

3. If you had a larger sample, how would you expect the confidence interval to be affected?