Question

Using traditional methods it takes 11.8 hours to receive a basic flying license. A new license training method using Computer Aided Instruction (CAI) has been proposed. A researcher used the technique on 9 students and observed that they had a mean of 11.4 hours with a standard deviation of 1.6. Is there evidence at the 0.05 level that the technique performs differently than the traditional method? Assume the population distribution is approximately normal.

Step 1 of 5: State the null and alternative hypotheses.

Step 2 of 5: Find the value of the test statistic. Round your answer to three decimal places.

Step 3 of 5: Specify if the test is one-tailed or two-tailed.

Step 4 of 5:

Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.

Step 5 of 5: Make the decision to reject or fail to reject the null hypothesis.

Answer 1

Given:

Sample size = n = 9

Sample mean = = 11.4

Standard deviation = s = 1.6

Significance level = = 0.05

1) The null hypothesis is

Ho : = 11.8

The alternative hypothesis is

Ha : 11.8

2) Since population standard deviation is unknown, we use t - test.

Test statistic is

t = /s/√n

= 11.4 - 11.8 /1.6/√9

= -0.75

Test statistic is t = -0.75

3) As alternative hypothesis contain sign, the test is two tailed test

4) Decision rule :

Degree of freedom = df = n-1 = 9-1 = 8

At 0.05 significance level, the critical value of t is

t/2,df = t0.05/2, 8 = 2.262

Critical value = 2.306

So decision rule is

Reject Ho, if t > 2.306 or t < -2.306

Since t = -0.75 > -2.306 , we fail to reject null hypothesis.

5) ​​​​​​Decision : Fail to reject the null hypothesis.

Conclusion : There is not sufficient evidence at the 0.05 level that the technique performs differently than the traditional method.