A certain random variable is normally distributed. Twenty-six observations were made independently and randomly, yielding a sample mean of 31, and standard deviation of 4.2. Test the hypothesis that these scores came from a population with a mean of 28.6.
Solution :
= 28.6
=31
S =4.2
n = 26
This is the two tailed test .
The null and alternative hypothesis is ,
H0 : =
28.6
Ha :
28.6
Test statistic = t
= (
-
) / S /
n
= (31- 28.6) / 4.2 /
26
= 2.914
Test statistic = t = 2.914
P-value =0.0074
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