Question

Using traditional methods it takes 107 hours to receive an advanced flying license. A new training technique using Computer Aided Instruction (CAI) has been proposed. A researcher believes the new technique may reduce training time and decides to perform a hypothesis test. After performing the test on 50 students, the researcher decides to reject the null hypothesis at a 0.10 level of significance.

What is the conclusion?
A. There is sufficient evidence at the 0.020 level of significance that the new technique reduces training time.
B. There is not sufficient evidence at the 0.02 level of significance that the new technique reduces training time.

Answer 1

B. There is not sufficient evidence at the 0.02 level of significance that the new technique reduces training time.

Explanation:

We are given that using traditional methods it takes 107 hours to receive an advanced flying license.

A researcher believes the new technique may reduce training time and decides to perform a hypothesis test.

Let
`\mu` = average training time to receive an advanced flying license

So, Null hypothesis,
`H_0` :
`\mu \geq` 107 hours {means that the new technique doesn't reduce training time}

Alternate Hypothesis,
`H_A` :
`\mu` < 107 hours {means that the new technique may reduce training time}

Now, it is stated that after performing the test on 50 students, the researcher decides to reject the null hypothesis at a 0.10 level of significance.

As we know that if the test statistics value is rejected at a 10% level of significance, then it must not be rejected at the 0.02 level of significance.

This means that there is not sufficient evidence at the 0.02 level of significance that the new technique reduces training time because our null hypothesis has not been rejected.