Question

You wish to test the following claim at a significance level of α=0.02

      H0:μ=62.5
      H1:μ>62.5

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size 64 with mean 66.5 and a standard deviation of 12.7.

What is the test statistic for this sample? (Report answer accurate to 3 decimal places.)
test statistic =

What is the p-value for this sample? (Report answer accurate to 4 decimal places.)
p-value =

Answer 1

Solution :

= 62.5

=66.5

=12.7

n = 64

this is the two tailed test .  

The null and alternative hypothesis is ,

H₀ :   = 62.5

H_a : >62.5

Test statistic = z

= ( - ) / / n

= (66.5-62.5) / 12.7 / 64

z=2.520

P(z > 2.520) = 1 - P(z < 2.520) = 1 -0.9941=0.0059 ( using z table )

P-value = 0.0059

= 0.02

P-value <

0.0059<0.02

it is concluded that the null hypothesis is rejected.

Therefore, there is enough evidence to claim that