Question

Using traditional methods, it takes 11.7 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 23 students and observed that they had a mean of 12.1 hours with a standard deviation of 1.4. A level of significance of 0.05 will be used to determine if the technique performs differently than the traditional method. Assume the population distribution is approximately normal. Find the value of the test statistic. Round your answer to three decimal places.

Answer 1

Answer:

There is no evidence to said that the technique performs differently than the traditional method.

Step-by-step explanation:

First, we need to write the null and alternative hypothesis as:

H0: x = 11.7

H1: x ≠ 11.7

Where x is the population mean for the new method.

Taking into account that the population distribution is approximately normal and the standard deviation of the population is unknown, we can calculated the statistic as:

$t=\frac{x'-x}{\frac{s}{\sqrt{n} } }$

Where t follows a distribution t-student with n-1 degrees of freedom.

So, replacing x' by the mean of the sample, s by the standard deviation of the sample and n by the size of the sample, we get:

$t=\frac{12.1-11.7}{\frac{1.4}{\sqrt{23} } }=1.37$

Then, we can find the critical points as:

P(t<t1) = 0.025

P(t<t2) = 0.975

So, with 22 degrees of freedom, the critical point t1 and t2 are equal to -2.07 and 2.07 respectively.

Since 1.37 is between the critical points, we can't reject H0. it means that there is no evidence to said that the technique performs differently than the traditional method.