Question

The maen travel time of light Puerto princesa city -iloilo is said to be 1.5hours .A certain airfare company recorded 20 different flights actual travel time.the mean is 2 hours with a standard deviation of 0.6hours .

Answer 1

The following null and alternative hypotheses need to be tested:

$H_0:\mu=1.5$

$H_1:\mu\not=1.5$

This corresponds to a two-tailed test, for which a t-test for one mean, with unknown population standard deviation, using the sample standard deviation, will be used.

Based on the information provided, the significance level is $\alpha = 0.05,$ $df=n-1=19$ and the critical value for a two-tailed test is $t_c =2.093024.$

The rejection region for this two-tailed test is $R = \{t:|t|>2.093024\}.$

The t-statistic is computed as follows:

$$t=\dfrac{\bar{x}-\mu}{s/\sqrt{n}}=\dfrac{2-1.5}{0.6/\sqrt{20}}=3.7268$$

Since it is observed that $t=3.7268>2.093024=t_c,$ it is then concluded that the null hypothesis is rejected.

Using the P-value approach:

The p-value for two-tailed, $df=19$ degrees of freedom, $t=3.7268$ is $p= 0.001426,$ and since $p= 0.001426<0.05=\alpha,$ it is concluded that the null hypothesis is rejected.

Therefore, there is enough evidence to claim that the population mean $\mu$

is different than 1.5, at the $\alpha = 0.05$ significance level.