Question

You wish to test the following claim ( H 1 ) at a significance level of α = 0.10 . H o : μ = 55.7 H 1 : μ < 55.7 You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n = 6 with a mean of ¯ x = 53.5 and a standard deviation of s = 5.9 . What is the critical value for this test? (Report answer accurate to three decimal places.) critical value =

Answer 1

Solution :

= 55.7

=53.5

s =5.9

n = 6

This is the left tailed test .

The null and alternative hypothesis is ,

H0 :    = 55.7

Ha : < 55.7

Test statistic = t

= ( - ) / s / n

= (53.5-55.7) / 5.9 / 6

= -0.913

Test statistic = t = -0.913

= 0.10

The critical value = - 1.476

P-value =0.2015

= 0.10

P-value >

0.2015 > 0.10

Fail to reject the null hypothesis .

There is insufficient evidence to suggest that