Question

Using traditional methods it takes 11.411.4 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 on 2424 students and observed that they had a mean of 11.211.2 hours with a standard deviation of 1.41.4. Is there evidence at the 0.10.1 level that the technique reduces the training time? Assume the population distribution is approximately normal.

Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.

H0: μ≥11.4

Ha: μ<11.4

t=−0.700

One-Tailed Test

Answer 1

Given :-

Mean () = 11.2

Standard deviation (s) = 1.4

Sample size (n) = 24

Test Hypothesis :

H0: u ≥11.4

Ha: u < 11.4

Rejection Region

Based on the information provided, the significance level is alpha = 0.1, and the critical value for a left-tailed test is tc =−1.319

The rejection region for this left-tailed test is

R= {t : t <−1.319}

Test statistic :

t = -0.700

Decision rule :

Since it is observed that t= -0.700 ≥tc = -1.319 , then it is concluded that the null hypothesis is not rejected.