Question

a sample of 39 observations is selected from a normal population. The same mean is 43 and the population standard deviation is 6. Conduct the following test of hypothesis using the 0.02

b. What is the decision rule?

D.. What is your decision regarding H0? Reject or fail to reject?

E-2. Interpret the p-value? There is a ______ % chance of finding a z value this large by "camping error"

Answer 1

Solution Given data n = 39 Sample mean ( ) = 43 Population standard deviation (-) = 6 significance level (Q) = 0.02 Now to state the null and alternative Null hypothesis Ho : M= 45 Altes native hypothesis H.: M +45 This is a two-tailed test- (b) Decision gule Reject hun hypothesis it Izı >Z212 hypothesis :- Zala = 20.02 = Zo.o. 2212 = 2.33 Answer: Rejet Ho if ZL-2.326 0712>2.326 Now to find the test- statistic:- We know that The formula of test- statistic is given by z=hlon Ν z= 43-45 Ν = 61039 -2 N = 0.9608 z = -2.08

:: Test -statistic , Z = -2.08 Test-criteria Reject null hypothesis if 121 >7212 Where 2/2 = 20.02 Zal2 = 20.01 Zal2 = 2.33 121 > Zala = 1-2.081 < 2033 = 2.08 <2.33 I refore we fail to reject null hypothesis (Ho). Now to find the p-value :- This is a two-tailed test P-value = 2xP (2> 2.08 ) P-value = 2 x [-P12<2-08)] P-value = 2xſ1-0-9812] = 2 x 0.0188 = 0.0376 :. P-value = 0.0376 0.0376 xloo = 3.76 There is a 3.76% chance of finding "camping corrida" a z value this large by