Question

1. The following 10 observations are a random sample from a normal population. 7.4 7.1 6.5 7.6 6.3 7.2 8.1 6.8 7.1 7.5

a) Find the mean and standard deviation of this data.

b)(5marks)TestH0: μ=7.4versusH1: μ<7.4atα=0.05.

Answer 1

Solution:

x	x2
7.4	54.76
7.1	50.41
6.5	42.25
7.6	57.76
6.3	39.69
7.2	51.84
8.1	65.61
6.8	46.24
7.1	50.41
7.5	56.25
∑x=71.6	∑x2=515.22

a ) Mean ˉx=∑xn

=7.4+7.1+6.5+7.6+6.3+7.2+8.1+6.8+7.1+7.5/10

=71.6/10

=7.16

Sample Standard deviation S=√∑x2-(∑x)2nn-1

=√515.22-(71.6)210/9

=√515.22-512.656/9

=√2.564/9

=√0.284/9

=0.5337

b )This is the Left tailed test .

The null and alternative hypothesis is ,

H0 :    = 7.4

Ha : < 7.4

Test statistic = t

= ( - ) / S / n

= (7.16-7.4) / 0.53 / 10

= −1.432

Test statistic = t = −1.432

P-value =0.093

= 0.05  

P-value >

0.093 > 0.05

Fail to reject the null hypothesis .

There is insufficient evidence to suggest that