Question

A sample of size 81 is taken from a population with unknown mean and standard deviation 4.5. In a test of Ho: u = 5 vs. Ha: u < 5, if the sample mean was 4, which of the following is true? (i) We would reject the null hypothesis at a =0.01. (ii) We would reject the null hypothesis at a = 0.05. (iii) We would reject the null hypothesis at a = 0.10. O only (i) O only (iii) O both (i) and (ii) O both (ii) and (iii) O all of them

Answer 1

null hypothesis:Hou Alternate Hypothesis:Ha u -1.645 for 0.05 level with left tail test, critical z= Decision rule:reject Ho if test statistic z<-1.645 population mean = sample mean 'x= sample size n= std deviation or std error ='ox=0/Vn= test stat z = '(X-)*vn/o= p value = 4.000 81.00 4.50 0.5000 -2.00 0.0228

since p value <0.1 and 0.05 , therefore we reject at 0.1 and 0.05 level

correct option is : both (ii) and (iii)