Question

Does Mars, Incorporated use the same percentage of red candies in its plain and peanut varieties? A random sample of 200 plain M & Ms contained 42 red candies and a random sample of 240 peanut M & Ms contained 68 red candies. Assume that the samples are independent.

1. Construct and interpret a 95% confidence interval for the difference between the parameters of interest.

2. Do the data indicate a difference in the percentage of red candies for plain and peanut M & Ms? Use .

3. Do the data indicate that plain M & M candies contain a smaller percentage of red candies? Use .

Answer 1

1)

We know that the 95% confidence interval for difference of proportions is given by:

We can say with 95% confidence that the difference between the true proportions will lie in this interval.

2)

The null and alternate hypothesis are:

H0:

Ha:

Since the 95% CI contains the value 0, so we cannot reject H0 at 5% level of significance.

Thus, the data does not indicate a difference in the percentage of red candies for plain and peanut M&Ms.

3)

The null and alternate hypothesis are:

H0:

Ha:

Since the 95% CI contains the value 0 and also some positive values, so we cannot reject H0 at 5% level of significance.

Thus, the data does not indicate that plian M&Ms contain a smaller percentage of red candies.

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