Question

The consumption rates of two aviation fuels, A and B, are compared. The sample from fuel A have 12 specimens with a mean burning rate of 21 cm/s and the sample from fuel B have 10 specimens with a mean burning rate of 18 cm/s. If the standard deviation in burning rates of the fuels are 3.5 cm/s and 3 cm/s for fuel A and fuel B, respectively, test the hypothesis that the burning rate of fuel A is more than that of fuel B by at least 2.5cm/s. Use ? = 0.05.

a. Write the appropriate hypothesis.

b. Use P-value approach for hypothesis testing.

c. Use z-test for hypothesis testing.

d. Use confidence interval for hypothesis testing.

e. Clearly write your conclusion.

f. If the true difference in the mean burning rates is ?? ′ − ?? ′ = 3 cm/s, find the type II error.

g. What is the minimum sample size needed to recognize the true mean burning rate ?? ′ − ?? ′ = 3 cm/s for ? = 0.05, and ? = 0.05.

Answer 1

(there are more than 4 subparts, as per policy i am answering first 4 parts)

a.

b.

c.

d.

since it is enitirely positive the claim mean 1 is greater than mean 2 is accepted, therefore null hypothesis is rejected

(please UPVOTE)