5. A sample of 16 cookies is taken to test the claim that each cookie contains a

Question

5. A sample of 16 cookies is taken to test the claim that each cookie contains at least 9 chocolate chips. The average number of chocolate chips per cookie in the sample was 7.875 with a standard deviation of 1. Assume the distribution of the population is normal. a. State the null and alternative hypotheses. b. Using a critical value, test the hypothesis at the 1% level of significance. c. Using a p-value, test the hypothesis at the 1% level of significance. d. Compute the probability of a Type II error if the true number of chocolate chips per cookie is 8.

Explanation / Answer

a.H0:9Ha:< 9

b.Test Stat:t= (_x- ) / (s /n) = (7.875- 9) / (1 /16 ) = 1.125 / 0.25=4.5Conclusion: Reject H0, -4.5 < 2.602

c.Reject H0; the p-value is less than 0.005.We don’t know the exact p-value becausewe are using a t-stat.But from the t-table we know that it is < 0.005.We know thisbecause in the row with dof = 15 the larger value of t given is 4.073 and our test stat iseven bigger than this.This is at the 99.9% confidence level, so = 0.001, but since ourtest is one sided we only take half of this value.

d. A Type II error has not been committed since H0 was rejected.

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