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: $u=30$

Alternative hypothesis: $u\not =30$

$\alpha = 0.02$

Test statistic:

$$Z = {\frac {(x - u)*\sqrt{n}} {s}}$$

where x - sample mean, s - sample standart deviation(square root of the variance) , n - sample size.

In our case $Z={\frac {(31.8-30)*5} {4}}=$ 2.25

p-value: $p=2P(Z>2.25)=2*0.01222=0.02444$

p-value is greater than significance level, so there is no evidence to reject the null hypothesis that the population mean baggage weight is equal to 30.