Question

State whether each statement is true or false?

Ho: u=150
H1: u (not equal to) 150
5% significance level

A.) Rejection region= t>0.03

B.) If true population mean is 150 . Then the propability its even more is 0.03.

C.) since p vaule is less than 0.05 we reject Ho at a 5% significance level

D.) If 90 % CI wa caculated using the same data.150 would be inside the confidence interval.

Answer 1

We have given the following information,

H_{​​​​​​0}​​​ :

H_{​​​​​​1} :

Level of significance is 5% therefore = 0.05 then

= 0.025 (Two sided hypothesis)

A.) Rejection region= t > 0.03

Ans.:- False (because it is two sided test hypothesis so rejection region = t > 0.025)

B.) If true population mean is 150. Then probability it's even more is o.o3.

Ans.:- False (if a population mean is 150. Then probability it's even less and even more both equal so it two sided hypothesis so probability it's even more is 0.025 not 0.03 )

C.) since p-value is less than 0.05, we reject H_{​​​​​0} at 5% significance level.

Ans.:- True ( if p-value is less than alpha then we reject the null hypothesis at given significance level.)

D.) If 90 % CI was caculated using the same data.150 would be inside the confidence interval.

Ans.) True ( beacuse confidence interval is nothing but the deviation from a true means so obviously 150 would be inside the confidence interval)