Question

After Halloween, Professor Lehavi’s, youngest son Dan, counted that 19 out of 100 of the M&Ms he received are green. The Mars company says that 22% of its M&Ms are green. Use Dan’s sample data to construct a 95% confidence interval estimate of the percentage of green M&Ms. Should Dan write an angry letter to Mars company? What is the alpha, what is the error, what is the final interval, what do you conclude about Dan writing a letter?

Answer 1

From standard normal tables, we have:
P(-1.96 < Z < 1.96) = 0.95

The sample proportion here is:
p = x/n = 0.19

Therefore the confidence interval here is computed as:

This is the required confidence interval here.

No Dan should not be angry here, as 0.22 lies in the above interval. The level of significance, alpha here is 1 - c = 0.05 that is 5%. As this level of significance we cannot reject the null hypothesis as the hypothesized value of 0.22 lies in the above interval.