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Using traditional methods, it takes 101 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 with 140 students and observed that they had a mean of 100 hours. Assume the standard deviation is known to be 6. A level of significance of 0.01 will be used to determine if the technique performs differently than the traditional method. Is there sufficient evidence to support the claim that the technique performs differently than the traditional method?

Respuesta :

Answer:

We conclude that there is not enough evidence to support the claim  compute technique performs differently than the traditional method.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 101 hours

Sample mean, [tex]\bar{x}[/tex] =100 hours

Sample size, n = 140

Alpha, α = 0.01

Population standard deviation, σ = 6 hours

First, we design the null and the alternate hypothesis

[tex]H_{0}: \mu = 101\text{ hours}\\H_A: \mu \neq 101\text{ hours}[/tex]

We use Two-tailed z test to perform this hypothesis.

Formula:

[tex]z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }[/tex]

Putting all the values, we have

[tex]z_{stat} = \displaystyle\frac{100 - 101}{\frac{6}{\sqrt{140}} } = -1.972[/tex]

Now, [tex]z_{critical} \text{ at 0.01 level of significance } = \pm 2.58[/tex]

Since,  

The calculated z statistic lies in the acceptance region, we fail to reject the null hypothesis and accept it.

We conclude that there is not enough evidence to support the claim that compute technique performs differently than the traditional method.

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