Question

You wish to test the following claim (H1) at a significance level of α=0.025

      Ho:μ=54.9
      H1:μ<54.9

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=38 with a mean of ¯x=52.7 and a standard deviation of s=15.3

What is the critical value for this test? (Report answer accurate to three decimal places.)
critical value =

Answer 1

Solution :

Given that ,

= 54.9

= 52.7

s = 15.3

n = 38

The null and alternative hypothesis is ,

H₀ :   = 54.9

H₁ : <  54.9

This is the two tailed test .

Test statistic = t

= ( - ) / s / n

= ( 52.7 - 54.9) / 15.3 / 38

= -0.36

The test statistic = -0.36

= 0.025

df = n - 1 = 38 - 1 = 37

t ,df = t_0.025,37 = -2.026

The critical value = -2.026