Question

Using traditional methods it takes 106 hours to receive an advanced flying license. A new training technique using Computer Aided Instruction (CAI) has been proposed. A researcher used the technique on 40 students and observed that they had a mean of 105 hours. Assume the population standard deviation is known to be 4. Is there evidence at the 0.02 level that the technique reduces the training time?

Step 1 of 6:

State the null and alternative hypotheses.

Step 2 of 6:

Find the value of the test statistic. Round your answer to two decimal places.

Step 3 of 6:

Specify if the test is one-tailed or two-tailed.

Step 4 of 6:

Find the P-value of the test statistic. Round your answer to four decimal places.

Step 5 of 6:

Identify the level of significance for the hypothesis test.

Step 6 of 6:

Make the decision to reject or fail to reject the null hypothesis

Please answer

Answer 1

Solution:

State the null and alternative hypotheses.

H0 : $\mu$ = 106

H1 :  $\mu$ < 106

Find the value of the test statistic.

The test statistic z is given by

z =
μο σ//n

= (105 - 106) / (4/$\sqrt{}$40)

= -1.58

The test statistic z = -1.58

Specify if the test is one-tailed or two-tailed.

One tailed (One tailed left sided)

Find the P-value of the test statistic

For left tailed test :

p value = P(Z < z)

= P(Z < -1.58)

= 0.0571 ..(use z table)

p value = 0.0571

Identify the level of significance for the hypothesis test.

$\alpha$ = 0.02

Make the decision

fail to reject the null hypothesis

(because p value is greater than $\alpha$ = 0.02)