Question

Using traditional methods it takes 103 hours to receive an advanced driving license. A new training technique using Computer Aided Instruction (CAI) has been proposed. A researcher used the technique on 230 students and observed that they had a mean of 104 hours. Assume the population variance is known to be 49. Is there evidence at the 0.1 level that the technique lengthens the training time?

Step 1 of 6 :

State the null and alternative hypotheses.

Answer 1

## Q ) Using traditional methods it takes 103 hours to receive an advanced driving license. A new training technique using Computer Aided Instruction (CAI) has been proposed. A researcher used the technique on 230 students and observed that they had a mean of 104 hours. Assume the population variance is known to be 49. Is there evidence at the 0.1 level that the technique lengthens the training time?

Answer :

We have given : n = sample size = 230  

xbar = sample mean = 104

μ = population mean = 103

σ^2 = population variance = 49 therefore ,

σ = known popualtion standard deviation = 7

α = 0.10 ( level of significance )

# Step 1 )  claim : Is there evidence at the 0.1 level that the technique lengthens the training time?

## step 2 ) state of the null and alternative hypothesis :

Ho : μ = 103 VS H1 : μ > 103

## step 3) Test Statistics :

Z = ( xbar - μ ) * √ (n) /  σ

Z = ( 104 - 103) * (15.1657) / 7

Z = 15 .1657 / 7

Z = 2.1665

## step 4 ) α value : 0.10 ( level of significance )

## step 5) critical value : here our test is one tailed test , and it is right tailed test

critical value = 1.282 ( used statistical table )

## step 6) Decision :

we reject Ho at ( 1 -  α ) * 100 % level of significance if test statistics value is greater than critical value ,

here Z stat > Z critical value , hence here we reject Ho at given level of signficance .

## Step 7 ) Conclusion :

There is sufficient evidence to conclude that   the technique lengthens the training time.

at 0.10 level of significance .