There is conflicting information about whether a new medication affects a person

Question

There is conflicting information about whether a new medication affects a person's ability to concentrate as measured by time spent on a task.

You wish to test the following claim (HaHa) at a significance level of =0.02=0.02. For the context of this problem, d=21d=2-1 where the first data set represents a pre-test measure of time on task and the second data set represents a post-test measure of time on task.

      Ho:d=0Ho:d=0
      Ha:d>0Ha:d>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:

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 =

The p-value is...

less than (or equal to)

greater than

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 greater than 0.

There is not sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is greater than 0.

The sample data support the claim that the mean difference of post-test from pre-test is greater than 0.

There is not sufficient sample evidence to support the claim that the mean difference of post-test from pre-test is greater than 0.

pre-test post-test 57.4 72.4 38.4 55.7 44.1 36.4 55 62.4 46.5 55.9 55.2 59.9 49.4 54.4 53.5 59.6

Explanation / Answer

Ans:

sample size,n=8

df=8-1=7

Test statistic:

t=(7.15-0)/(7.578/sqrt(8))=2.669

p-value=tdist(2.669,7,1)=0.0160

p-value<0.02,So,we Reject null hypothesis.

There is not sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is greater than 0.

pre-test post-test difference(d) 1 57.4 72.4 15 2 38.4 55.7 17.3 3 44.1 36.4 -7.7 4 55 62.4 7.4 5 46.5 55.9 9.4 6 55.2 59.9 4.7 7 49.4 54.4 5 8 53.5 59.6 6.1 mean= 7.15 std. dev= 7.578

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