Suppose you are interested in the true proportion of red Skittles. Your instructor will compile the data from the entire class and post the number of skittles of each color and the total number of Skittles that were observed below. Check the conditions for computing a 95% confidence interval for

Question

using the class data. State whether or not the conditions are met and whether you believe the results you obtain in step B will be valid. Note: Even though the bags of Skittles in the class data set were selected conveniently by students, the Skittles were placed into the bags using an objective device (the machinery at the factory).
Color Frequency
Red 196
Orange 188
Yellow 186
Green 194
Purple 213
TOTAL 977

Answer 1

To compute a 95% confidence interval for the true proportion of red Skittles, we need to check the following conditions:

1. Random sampling: The Skittles were selected conveniently by students, but they were placed into the bags using an objective device at the factory. This condition is met.

2. Large sample size: The total number of Skittles observed is 977, which is reasonably large. The sample size should be at least 10 times the number of red Skittles, which is 196 in this case. This condition is met.

3. Success-failure condition: The number of red Skittles (196) and non-red Skittles (781) are both greater than 10. This condition is also met.

Since all the conditions for computing a confidence interval for the true proportion of red Skittles are met, we can proceed with calculating the interval with confidence that the results obtained will be valid.