Question

Using traditional methods, it takes 11.111.1 hours to receive a basic driving license. A new license training method using Computer Aided Instruction (CAI) has been proposed. A researcher used the technique with 2424 students and observed that they had a mean of 10.710.7 hours with a standard deviation of 2.02.0. A level of significance of 0.050.05 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:

The value of the test statistic is -0.979

Step-by-step explanation:

We are given the following in the question:  

Population mean, μ = 11.1 hours

Sample mean, $\bar{x}$ = 10.7 hours

Sample size, n = 24

Alpha, α = 0.05

Sample standard deviation, s = 2.0 hours

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 11.1\text{ hours}\\H_A: \mu \neq 11.1\text{ hours}$

We use two-tailed t test to perform this hypothesis.

Formula:

$t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }$

Putting all the values, we have

$t_{stat} = \displaystyle\frac{10.7 - 11.1}{\frac{2}{\sqrt{24}} } = -0.979$

Thus, the value of the test statistic is -0.979