Question

A sample of 36 observations is selected from a normal population. The sample mean is 49, and the population standard deviation is 5. Conduct the following test of hypothesis using the 0.05 significance level

H₀: μ = 50

H₁: μ ≠ 50

1. e-1. What is the p-value? (Round your z value to 2 decimal places and final answer to 4 decimal places.)

   e-2. Interpret the p-value? (Round your z value to 2 decimal places and final answer to 2 decimal places.)

Answer 1

Solution :

The null and alternative hypothesis is,

H₀ :   = 50

H_a :    50

= 49

= 5

n = 36

Test statistic = z =

= ( - ) / / n

= (49 - 50) / 5 / 36

= -1.20

P( Z< -1.20)

= 0.1151

This is the two tailed test .

P-value = 2 * P( Z< -1.20)

P-value = 2 * 0.1151

= P-value = 0.2302

= 0.05  

Fail to rejected null hypothesis because p-value more than 0.05