Question

You wish to test the following claim (HaHa) at a significance level of α=0.02α=0.02. 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 the following sample of data:

pre-test	post-test
51.7	4.2
57	33.6
34.7	12.7
44	16.3
25.3	10.3
48	47.3

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

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

The test statistic is...

• in the critical region
• not in the critical region

This test statistic leads to a decision to...

• reject the null
• accept the null
• fail to reject the null

As such, the final conclusion is that...

• There is sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is less than 0.
• There is not sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is less than 0.
• The sample data support the claim that the mean difference of post-test from pre-test is less than 0.
• There is not sufficient sample evidence to support the claim that the mean difference of post-test from pre-test is less than 0.

Answer 1

Leh Md and ơd denote nespeeri very sha n d and me popul a hon. and γη e an pe - est posh -est scores frrom SeoreS. Heve the null and altennative hypothe ses ave Heve 0is unknown and he popul ahion of difevence store s So, we perfoem teS

the test is Left -aaiLed est, o , (n-I) As Here d is Leve L of sign i fi c a n e e andnis the al number of Poivs of values of pre - besh scores and pos-est scoves Given that, d0 2 Here n6 0.02; (6-1 0 0 2,5 2 757. The res shah she is where D and Sp denohe sample mean and sample sran d ard deviahion of difference of posh -te s+ pes frrom pre- resh scores scores ompee

dis he vaue of M under Ho pre- kest post-b rest dd 47.5 2 25 25 23.4 547.5 4.2 33.6 12.7 16 3 10 3 47 3 51.7 ら1 34.7 484 27.7 767 29 25.3 - 15 2 25 48 -0 7 0 49 -136.3 4280 59 Now Vn 13 6 3 2 2 717 4280.53- (-136.3)2. 236 8 6 2 Note that d and denote vespechivel the obse nved vawes oFD and

he ousenve valine of the est stahishe is :「(- 22.717-o ) [Under" H 23 6 86 2 3.616 The emheal ne gion is WTT42 757 Nore hhat, he 3 6162 757. So, he Hesh shahishe is in he eon We kno w He e e To 3 616 2 757to 0.02; 5

o, e weject the nul hyporhesis The sample datm support evenee of Post - He s pre - he shis Less han 0