The Mars Company (the makers of M&Ms) takes quality control very seriously. In p

Question

The Mars Company (the makers of M&Ms) takes quality control very seriously. In particular, it has strict guidelines for the proportion of M&M’s produced of each color (Blue, Red, Green, Brown, and Orange). We will use confidence intervals to develop interval estimates for the proportion of blue M&Ms, to determine if the Mars Company meets its quality control standards.

In this activity, we'll investigate the proportion of M&M's that are blue. To get an estimate of this proportion, we need to take a sample. The sample proportion is subject to chance variability and we can express this by providing a confidence interval. Each group gets a sample of M&Ms (an independent random sample). We want to estimate the population proportion of blue M&M’s among all M&M’s produced.

1) Define an individual in the study.

2) Define the population of interest and the parameter p being estimated in the context of the problem. (Note you cannot calculate the parameter, but you can verbally define what it measures)

3) State your research question in the context of the problem.

Explanation / Answer

(a) It is given that different random samples are collected and given to number of groups with 1 group getting 1 random sample.

Hence, an individual under study in this case would be any group geting a random sample of M&Ms.

(b) The populaion of interest here is the grand total M&Ms produced by the company of each color (Blue, Red, Green, Brown, and Orange).

The parameter to estimate, namely p, is the proportion of Blue colored M&Ms produced by the company in any batch of production out of total M&Ms produced of each color (Blue, Red, Green, Brown, and Orange).

For example, if total M&Ms produced of each color (Blue, Red, Green, Brown, and Orange) is 100 and number produced of blue color is 25, then p = 0.25

(c) The basic questions are: Are the strict guidelines being followed for proportion being under control of Blue Color M&Ms. This translates to Research question as:

We need to test Hypothesis H0 : p = p0 against alternative H1: p is not equal to p0,

where p0 is the proportion of Blue color M&Ms as given by strict quality control guidelines.

Also, We want to estimate the population proportion of blue M&M’s among all M&M’s produced. Hence, we want to estimate the value of p and also would be interested in Confidence Interval of p with 95% level of Confidence.

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