Answer to Question #321573 in Statistics and Probability for lae

Question

the mean weight of baggage of 25 passengers from USA bound for the Philippines is 31.8 kilos with a variance of 16. test the claim that the population mean baggage weight is equal to 30 kilos at 0.01 level of significance. Assume that the population is normally distributed. The t value is 2.492

Answer 1

Solution:

$X=31.8kg$ - sample mean;

$\sigma=\sqrt{var}=\sqrt{16}=4;$ - standard deviation;

$n=25;$ - sample size;

$\alpha=0.01$ - significance level;

$\mu=30$ - test population mean;

Let's z check now when $\mu=30;$

$z=\frac{31.8-30}{4}\times\sqrt{25}=2.25;$

Check p value:

$p=2P(z>2.5)=2\times0.0122=0.0244;$

Answer:

$p>\alpha$, so there is no evidence to reject the null hypothesis that the population mean baggage weight is equal to 30