A manufacturer claims tha a fuel additive it produces will yield an increase of

Question

A manufacturer claims tha a fuel additive it produces will yield an increase of at least 4 mpg for a mid-sized car. A consumer group investigates this claim with a random sample of 12 mid-sized cars. The sample results had a mean increase of 3.7926 mpg and a standard deviation of 0.4 mpg. Assume the mpg increases form a normal distribution. The consumer group will test if the sample data is extreme enough to reject the manufacturer's claim.

A.) What is the parameter of interest in the context of this problem? State appropriate symbol.

B.) State the null and alternative hypothesis for the consumer group.

C.) What are the possible decisions here?

D.) Clearly describe the Type I and Type II errors for this test in the context of this problem.

Explanation / Answer

(A) Parameter: Mean increase in the mpg

(B) Ho: 4 versus Ha: < 4

(C) Possible decisions are to reject Ho and conclude that < 4 or not reject Ho and conclude that 4

(D) Type I error: Concluding that < 4 while in fact 4

Type II error: Concluding that 4 while in reality < 4

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