Question

using traditional methods, it takes 10.0 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 26 students and observed that they had a mean of 10.4 hours with a variance of 2.89. 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.
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Explanation:

Step1: Identify the formula for t - test statistic

For a one - sample t - test, the formula is $t=\frac{\bar{x}-\mu}{s/\sqrt{n}}$, where $\bar{x}$ is the sample mean, $\mu$ is the population mean, $s$ is the sample standard deviation, and $n$ is the sample size.

Step2: Calculate the sample standard deviation

Given the variance $s^{2}=2.89$, then the sample standard deviation $s = \sqrt{2.89}=1.7$.

Step3: Identify the values of $\bar{x}$, $\mu$ and $n$

We have $\bar{x}=10.4$, $\mu = 10.0$, and $n = 26$.

Step4: Substitute the values into the formula

$t=\frac{10.4 - 10.0}{1.7/\sqrt{26}}=\frac{0.4}{1.7/\sqrt{26}}$.
First, calculate $1.7/\sqrt{26}\approx1.7/5.099\approx0.333$.
Then $t=\frac{0.4}{0.333}\approx1.201$.

Answer:

$1.201$