Question

A sample of 15 measurements, randomly selected from a normally distributed population, resulted in a sample mean, x¯¯¯=6.1 and sample standard deviation s=1.92. Using α=0.1, test the null hypothesis that μ≥6.4 against the alternative hypothesis that μ<6.4 by giving the following.

a) The number of degrees of freedom is: df= .

b) The critical value is: tα= .

c) The test statistic is: ttest=

Answer 1

Solution:

Given that,

= 6.4

= 6.1

s = 1.92

n = 15

a) The number of degrees of freedom is: df= .1 - n = 1 - 15 = 14

b) The critical value

= 0.1

  / 2 = 0. 1 / 2 = 0.05

t _/2,df = t_0.05,14 =1.761

The critical value is: 1.761

c) The test statistic is t

t = ( -  ) /  (s /n)

t =( 6.1 - 6.4) / (1.92 / 15)

t = ( - 0.3 *  15 ) / 1.92

t = -0.605

Test staistic = - 0.605

P value = 0.7226

P value >  

0.7226 > 0.1

Do not reject the null hypothesis .