Question

Using traditional methods, it takes 9.1

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 11
students and observed that they had a mean of 9.3
hours with a standard deviation of 1.3
. 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

To test if a new license training method using Computer Aided Instruction (CAI) performs differently from the traditional method, we can conduct a hypothesis test using the mean and standard deviation values provided. The test statistic is approximately 0.509.

Step-by-step explanation:

To test if the new license training method using Computer Aided Instruction (CAI) performs differently than the traditional method, we can conduct a hypothesis test. First, we need to state the null and alternative hypotheses. The null hypothesis is that the mean time to receive a basic flying license using the CAI method is the same as the traditional method (μ = 9.1 hours). The alternative hypothesis (Ha) is that the mean time using the CAI method is different from the traditional method (μ ≠ 9.1 hours).

Next, we can calculate the test statistic using the formula:

t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))

Plugging in the values from the question, we get:

t = (9.3 - 9.1) / (1.3 / sqrt(11))

t = 0.2 / (1.3 / 3.3166)

t = 0.2 / 0.3927

t ≈ 0.509

Therefore, the value of the test statistic is approximately 0.509 (rounded to three decimal places).