Question

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. Please give the answers clearly labeled in order. Thanks :)

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.

Answer 1

Sample size = n = 16

Sample mean = = 7.875

Sample standard deviation = s = 1

a) Claim: each cookie contains at least 9 chocolate chips.

The null and alternative hypothesis is

b) Level of significance = 0.01

Degrees of freedom = n - 1 = 16 - 1 = 15

Critical value = 2.602 ( Using t table)

Here population standard deviation is unknown so we have to use t-test statistic.
Test statistic is

c) P-value = P(T > 4.5) = 0.0002

P-value < 0.01 we reject null hypothesis.

Conclusion:

each cookie contains at least 9 chocolate chips.