Question

Suppose a car dealer tells you that specific cars get 35 miles per gallon on average. You would be able to use hypothesis tests to test whether or not this value might be correct. Why would you use a hypothesis test instead of a confidence interval in this situation?

1. Answer the following questions in a Word document:
   • A car dealer states that a new brand of car gets 35 miles per gallon on average. Suppose a consumer group claims that these cars get less than 35 miles per gallon. Set up the null and alternative hypotheses for this example.
   • The average daily rainfall in a jungle in South America was four inches back in 2000. Suppose a scientist thinks the average rainfall is different now. Set up the null and alternative hypotheses for this example.

Answer 1

(a)

Question:

Suppose a car dealer tells you that specific cars get 35 miles per gallon on average. You would be able to use hypothesis tests to test whether or not this value might be correct. Why would you use a hypothesis test instead of a confidence interval in this situation?

Answer:

Here the question is whether to reject or accept our estimate that specific cars get 35 miles per gallon on average. In such situations involving decision as to accept or reject, hypothesis testing is preferred because hypothesis testing allows us, at a given confidence level, conclusively to reject or accept our estimate.

(b)

Question:

A car dealer states that a new brand of car gets 35 miles per gallon on average. Suppose a consumer group claims that these cars get less than 35 miles per gallon. Set up the null and alternative hypotheses for this example.

Answer:

H0: Null Hypothesis: = 35 (A new brand of car gets 35 miles per gallon on average)

HA: Alternative Hypothesis: < 35 (These cars get less than 35 miles per gallon) (Claim)

(c)

Question:

The average daily rainfall in a jungle in South America was four inches back in 2000. Suppose a scientist thinks the average rainfall is different now. Set up the null and alternative hypotheses for this example.

Answer:

H0: Null Hypothesis: = 4 (The average daily rainfall in a jungle in South America was four inches back in 2000)

HA: Alternative Hypothesis: 4 ( The average rainfall is different now) (Claim)