Question

Using traditional methods, it takes 11.9 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 9 students and observed that they had a mean of 12.2 hours with a standard deviation of 1.5. 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

The test statistic calculated for the hypothesis testing to compare a new flying license training technique with the traditional method is 0.6.

Step-by-step explanation:

The calculation of the test statistic for a sample where we are testing whether a new teaching method impacts the time to receive a flying license involves the mean of the traditional method (the population mean), the sample mean, sample standard deviation, and the sample size. Here's how to compute the test statistic using a one-sample t-test:

1. First, identify the sample mean (Ü), population mean (μ), sample standard deviation (s), and sample size (n).
2. Then, use the t-test formula: t = (Ü - μ) / (s / √n).
3. Puting the values into the formula, we get:
   t = (12.2 - 11.9) / (1.5 / √9)
4. Calculate the denominator: 1.5 / √9 = 1.5 / 3 = 0.5.
5. Calculate the numerator: 12.2 - 11.9 = 0.3.
6. Finally, t = 0.3 / 0.5 = 0.6.

The value of the test statistic is 0.6 (rounded to three decimal places).