Question

Consider the following matched-pairs sample that represents observations before and after an experiment. Assume that the sample differences are normally distributed. Hint: The differences are calculated as Xafter - Xbefore. (You may find it useful to reference the appropriate table: z table or t table) Before After 2.5 2.9 1.8 3.1 1.4 -2.9 3.9 -1.8 1.2 -1.9 -3.1 0.2 0.6 2.5 2.5 2.9 Click here for the Excel Data File a. Construct the competing hypotheses to determine if the experiment increases the value of the observations. HO: HD = 0; HA: MD = 0 HO: MD 2 0; HA: UD < 0 HO: HD SO; HA: MD > 0 b. Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round all intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) Test statistic

Answer 1

(a)

Here we are to test if the after value is more. Hence the correct set of hypotheses is given in third option. The correct option is third option

(b)

The table is made as

Before	After	Difference
2.5	2.9	0.4
1.8	3.1	1.3
1.4	3.9	2.5
-2.9	-1.8	1.1
1.2	0.2	-1
-1.9	0.6	2.5
-3.1	2.5	5.6
2.5	2.9	0.4

The data is summarized as follows:

Sample Size(n)	8
Sample mean ()	1.6
Sample SD(s)	1.985663=1.9857

The test statistic is given by

(c)

The test statistic follows t distribution with df 7 under the null hypothesis. The p-value is obtained as 0.02836 . Thus the correct option is the third option

(d)

We reject H0. At the 5% significance level, we can conclude that the experiment increases the value of the observations.

(e)

The p-value is less than 0.05 and hence the null hypothesis is rejected at 5% level of significance. But the p-value is more than 0.01 and hence the null hypothesis cannot be rejected at 1% level of significance. Hence the correct answer is yes

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