Question

Please show all work!

2. You are given the following : Claim sizes follow a normal distribution with mean i and variance o2 = 47, 300. The hyp otheses are . H : μ = 10000 , Hau<10000 One claim of 9,600 is observed Determine the test result. Show me the computation process Reject Ho at the 0.01 significance level Reject Ho at the 0.02 significance level, but not at the 0.01 level Reject Ho at the 0.05 significance level, but not at the 0.02 level. Reject Ho at the 0.10 significance level, but not at the 0.05 level. Do not reject Ho at the 0.10 significance level.

Answer 1

Given

$X\sim N(10000,47300)$

then

$z= \frac{X-10000}{\sqrt{47300}}\sim N(0,1)$

$P(X<9600)= P(z<\frac{9600-10000}{\sqrt{47300}})$

= P( z < -1.84 )

= 0.0329

Therefore , P value = 0.0329 is the probability of getting the observed value (9600) given that $\mu =10000$

P value > 0.02

Fail to reject H0 at 0.02 significance level

P value < 0.05

Reject H0 at 0.05 significance level , but not at 0.02 level

Note : If P value < significance level , we reject H0 at that significance level.