Solution:
x | x2 |
22 | 484 |
12.5 | 156.25 |
6 | 36 |
8.5 | 72.25 |
12 | 144 |
3 | 9 |
14.5 | 210.25 |
22 | 484 |
10 | 100 |
4 | 16 |
∑x=114.5 | ∑x2=1711.75 |
Mean ˉx=∑xn
=22+12.5+6+8.5+12+3+14.5+22+10+4/10
=114.5/10
=11.45
Sample Standard deviation S=√∑x2-(∑x)2nn-1
=√1711.75-(114.5)210/9
=√1711.75-1311.025/9
=√400.725/9
=√44.525
=6.6727
This is the left tailed test .
The null and alternative hypothesis is ,
H0 : = 16
Ha : < 16
Test statistic = t
= ( - ) / S / n
= (11.45-16) / 6.67 / 10
= −2.157
Test statistic = t = −2.157
P-value =0.0297
= 0.05
P-value <
0.0297 < 0.05
Reject the null hypothesis .
There is sufficient evidence to suggest that the population mean μ is less than 16, at the 0.05 significance level.
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