Question

You are an intern with the Keebler elves, and you've been asked to check the claim that each cookie produced by the elves contains at least 9 chocolate chips, so you develop the following hypotheses:

• H₀: μ ≥ 9
• H_a: μ < 9

You pull a sample of 16 cookies, and find that the average number of chocolate chips for the cookies in the sample is 8.5 with a (sample) standard deviation of 1. (Also, past history has shown that the distribution of the population is normal.)

PART 1: If you use the p-value method to test your hypothesis, what would your p-value be (to 3 decimal places)?

PART 2: Based on your answer to PART 1, should you reject or not reject H₀ at the 0.01 level of significance?

PART 3: If you use the critical value method to test your hypothesis, what would your critical value be, at a 0.01 level of significance (to 3 decimal places)?  (Hint: This should be a negative number.)

PART 4: Based on your answer to PART 3, should you reject or not reject H₀ at the 0.01 level of significance?

PART 5: Based on your results from PART 2 & PART 4, what should you tell your leadership about your study?

Select one:

a. We cannot reject the null hypothesis, therefore it appears that the average number of chips per cookie is less than 9

b. We cannot reject the null hypothesis, therefore we assume that we are meeting our claim that each cookie has at least 9 chips in it

c. We reject the null hypothesis, therefore we assume that we are meeting our claim that each cookie has at least 9 chips in it

d. We reject the null hypothesis, therefore it appears that the average number of chips per cookie is less than 9

Answer 1