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 =0.002=0.002. 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:

pre-test post-test 45.4 77 48.7 53.4 43.3 66.1 40.5 58.5 37.7 52.8 39 42.4

42.4

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 either:

• less than (or equal to)

• greater than

This test statistic leads to a decision to either.

• reject the null

• accept the null

• fail to reject the null

pre-test post-test 45.4 77 48.7 53.4 43.3 66.1 40.5 58.5 37.7 52.8 39

42.4

Explanation / Answer

The statistical software output for this problem is:

Paired T hypothesis test:
D = 1 - 2 : Mean of the difference between post-test and pre-test
H0 : D = 0
HA : D > 0
Hypothesis test results:

Hence,

Test statistic = 3.621

P - value = 0.0076

The p - value is less than (or equal to)

This test statistic leads to a decision to reject the null

Difference Mean Std. Err. DF T-Stat P-value post-test - pre-test 15.933333 4.4001263 5 3.6211082 0.0076

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