Answer to Question #342080 in Statistics and Probability for jess

Question

The mean weight of the luggage carried into an airplane by individual passengers at Taguegarao City Airport is 19.8 kilograms. A statistician takes a random sample of 110 passengers and obtain a sample mean weight of 18.5 kilograms with standard deviation of 8.5 kilograms. Test the claim at a=0.01 level of significance.

Answer 1

The following null and alternative hypotheses need to be tested:

$H_0:\mu=19.8$

$H_a:\mu\not=19.8$

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 $\alpha = 0.01,$ $df=n-1=109$ degrees of freedom, and the critical value for a two-tailed test is $t_c =2.621688.$The rejection region for this two-tailed test is $R = \{t:|t|> 2.621688\}.$

The t-statistic is computed as follows:

$$t=\dfrac{18.5-19.8}{8.5/\sqrt{110}}=-1.6041$$

Since it is observed that $|t| = 1.6041<2.621688=t_c,$ it is then concluded that the null hypothesis is not rejected.

Using the P-value approach:

The p-value for two-tailed $df=109$ degrees of freedom, $t=-1.6041$ is $p=0.111586,$ and since $p=0.111586>0.01=\alpha,$ it is concluded that the null hypothesis is not rejected.

Therefore, there is not enough evidence to claim that the population mean $\mu$ is different than 19.8, at the $\alpha = 0.01$ significance level.