Question

Using traditional methods, it takes 8.1 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 8.2 hours with a standard deviation of 1.2. A level of significance of 0.1 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:

The value of the test statistic is 0.4.

Step-by-step explanation:

The value of the test statistic is given by:

Our test statistic is:

$t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is expected mean, $\sigma$ is the standard deviation and n is the size of the sample.

Using traditional methods, it takes 8.1 hours to receive a basic flying license.

This means that $\mu = 8.1$

A researcher used the technique with 23 students and observed that they had a mean of 8.2 hours with a standard deviation of 1.2.

This means that $n = 23, X = 8.2, \sigma = 1.2$

Find the value of the test statistic.

$t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$t = \frac{8.2 - 8.1}{\frac{1.2}{\sqrt{23}}}$

$t = 0.4$

The value of the test statistic is 0.4.