Question

#1

A candy company makes chocolates in two flavors, milk and dark. Brenda is a quality control manager for the company who wants to make sure that each jumbo bag contains about the same number of chocolates, regardless of flavor. She collects two random samples of 15 bags of chocolates from each flavor and counts the number of chocolates in each bag. Assume that both flavors have a standard deviation of 9.5 chocolates per bag and that the number of chocolates per bag for both flavors is normally distributed. Let the number of milk chocolates be the first sample, and let the number of dark chocolates be the second sample.

She conducts a two-mean hypothesis test at the 0.01 level of significance, to test if there is evidence that both flavors have the same number of chips in each bag.

For this test: H0:μ1=μ2; Ha:μ1≠μ2, which is a two-tailed test.

The test results are: z≈3.99 , p-value is approximately 0.000

Which of the following are appropriate conclusions for this hypothesis test? Select all that apply.

A. Fail to reject H0

B. Reject H0.

C. There is sufficient evidence at the 0.01 level of significance to conclude that the mean number of chocolates per bag for milk chocolates is different the mean number of chocolates per bag for dark chocolates.

D. There is insufficient evidence at the 0.01 level of significance to conclude that the mean number of chocolates per bag for milk chocolates is different than the mean number of chocolates per bag for dark chocolates.

Answer 1

Solution:

Given: A candy company makes chocolates in two flavors, milk and dark.

Sample 1 Milk:

Sample size = n₁ =15 bags

Population Standard Deviation= chocolates per bag

Sample 2 dark:

Sample size = n₂ =15 bags

Population Standard Deviation= chocolates per bag

level of significance = 0.01

We have to test if there is evidence that both flavors have the same number of chips in each bag.

For this test: H0:μ1=μ2; Ha:μ1≠μ2, which is a two-tailed test.

The test results are: z≈3.99

p-value is approximately 0.000

We have to make appropriate conclusions for this hypothesis test.

Decision Rule:
Reject null hypothesis H0, if P-value < 0.01 level of significance, otherwise we fail to reject H0

Since p-value is approximately 0.000 < 0.01 level of significance, we reject null hypothesis H0.

Thus correct option is B.

Now for conclusion:

Since we have rejected null hypothesis H0, thus mean  number of chocolates per bag for milk chocolates and dark chocolates are different

thus correct conclusion is:

C. There is sufficient evidence at the 0.01 level of significance to conclude that the mean number of chocolates per bag for milk chocolates is different the mean number of chocolates per bag for dark chocolates.

Thus correct options are:

B. Reject H0.

C. There is sufficient evidence at the 0.01 level of significance to conclude that the mean number of chocolates per bag for milk chocolates is different the mean number of chocolates per bag for dark chocolates.