Question

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.

Answer 1

Solution :

=  28.6

=31

S =4.2

n = 26

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :    = 28.6

H_a :      28.6

Test statistic = t

= ( - ) / S / n

= (31- 28.6) / 4.2 / 26

= 2.914

Test statistic = t = 2.914

P-value =0.0074