Question

A sample of 31 observations is selected from a normal population. The sample mean is 23, and the population standard deviation is 2. Conduct the following test of hypothesis using the 0.10 significance level. H0: μ ≤ 22 H1: μ > 22 Is this a one- or two-tailed test? One-tailed test Two-tailed test What is the decision rule? Reject H0 when z > 1.282 Reject H0 when z ≤ 1.282 What is the value of the test statistic? (Round your answer to 2 decimal places.) What is your decision regarding H0? Reject H0 Fail to reject H0 e-1. What is the p-value? (Round your answer to 4 decimal places.) e-2. Interpret the p-value? (Round your final answer to 2 decimal places.)

Answer 1

x̅ =   23      
σ =   2      
n =   31      
α =    0.10
  
Null and Alternative hypothesis:          
Ho : µ <=   22      
H1 : µ >   22

This is a one tailed test.
          
Critical value :          
At α = 0.10, right tailed critical value, z crit = ABS(NORM.S.INV( 0.10) =   1.282  

Reject Ho if z > 1.282
          
Test statistic:          
z = (x̅- µ)/(σ/√n)

= (23- 22)/(2/√31) = 2.78
          
Decision:          
Reject Ho.

p-value = 1- NORM.S.DIST( 2.7839 ,1 ) =   0.0027