Answer to Question #240943 in Statistics and Probability for Matilda

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 0.02 level of significance.

Answer 1

Null hypothesis $H_0:\mu=30.$

Alternative hypothesis $H_a:\mu\ne30.$

Test statistic: $z=\frac{31.8-30}{\sqrt{\frac{16}{25}}}=2.25.$

P-value: $p=2P(Z>2.25)=0.0244.$

Since the p-value is greater than 0.02, fail to reject the null hypothesis.

There is no significant evidence that the population mean baggage weight is not equal to 30 kilos.