Question

using traditional methods it takes 102 hours to receive an advanced flying license. A new training technique using computer aided inctruction has been proposed. A researcher used the technique on 60 students and observed that they had a mean of 100 hours. Assume the population variance is known to be 36. Is there evidence at the 0.05 level of the technique performs differently than the traditional method?

what is H0 =?

what is Ha=?

what is the value of the test statistic? is this two or one tailed?? Please help me!!!

Answer 1

Here, we have to use one sample z test for the population mean.

The null and alternative hypotheses are given as below:

Null hypothesis: H0: A new training technique using computer aided instruction performs same as the traditional method.

Alternative hypothesis: Ha: A new training technique using computer aided instruction performs differently than the traditional method.

H0: µ = 102 versus Ha: µ ≠ 102

This is a two tailed test.

The test statistic formula is given as below:

Z = (Xbar - µ)/[σ/sqrt(n)]

From given data, we have

µ = 102

Xbar = 100

σ = sqrt(36) = 6

n = 60

α = 0.05

Critical value = -1.96 and 1.96

(by using z-table or excel)

Z = (100 - 102)/[6/sqrt(60)]

Z = -2.5820

P-value = 0.0098

(by using Z-table)

P-value < α = 0.05

So, we reject the null hypothesis

There is sufficient evidence to conclude that a new training technique using computer aided instruction performs differently than the traditional method.