Question

You wish to test the following claim (HaHa) at a significance level of α=0.10α=0.10. For the context of this problem, μd=μ2−μ1μd=μ2-μ1 where the first data set represents a pre-test and the second data set represents a post-test.

      Ho:μd=0Ho:μd=0
      Ha:μd<0Ha:μd<0

You believe the population of difference scores is normally distributed, but you do not know the standard deviation. You obtain pre-test and post-test samples for n=20n=20 subjects. The average difference (post - pre) is ¯d=−7.1d¯=-7.1 with a standard deviation of the differences of sd=15.8sd=15.8.

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =

What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =

Answer 1

Given, to test,

Vs

Sample size, n= 20

Level of significance, =0.10

The average difference (post - pre),   = -7.1

Standard deviation of the differences, = 15.8

Test statistic:

  

  

(calculated)

(table value)

Since, , is one sided, we see the value in table corresponding to n=19 and probability 2*0.1 = 0.2

Further, the p-value for this sample is,

Hence, p- value = 0.02942 = 0.03 (approximately)

Decision: Since, p-value < , i.e., 0.1 > 0.03, we reject H0 at 0.1 level of significance.