Question

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

H o : μ = 56.9

H a : μ > 56.9 H

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n = 24 with mean M = 63 and a standard deviation of S D = 18.6 . What is the test statistic for this sample? (Report answer accurate to three decimal places.)

test statistic =

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

p-value =

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is ,

H₀ :   = 56.9

H_a : > 56.9

Solution :

Given that ,

= 63

= 56.9

s = 18.6

n = 24

df = 24 - 1 = 23

Test statistic = t

= ( - ) / s / n

= (63 - 56.9) / 18.6 / 24

= 1.606

Test statistic = 1.606

P-value = 0.061