40. Stress level were recorded during a true answer and a false answer given by

Question

40. Stress level were recorded during a true answer and a false answer given by each of six people in a study of lie-detecting equipment, based on the idea that the stress involved in telling a lie can be measured. The results are shown in Table 10.7.5

Vocal Stress Level

Preson

True Answer

False Answer

1

12.8

13.1

2

8.5

9.6

3

3.4

4.8

4

5.0

4.6

5

10.1

11.0

6

11.2

12.1

a. Was everyone's stress level higher during a false answer than during a true answer?

b. Find the average stress levels for true and for false answers. Find the average change in stress level (false minus true).

c. Find the appropriate standard error for the average difference. In particular, is this a paired or an unpaired situation?

Vocal Stress Level

Preson

True Answer

False Answer

1

12.8

13.1

2

8.5

9.6

3

3.4

4.8

4

5.0

4.6

5

10.1

11.0

6

11.2

12.1

Explanation / Answer

Stress level were recorded during a true answer and a false answer given by each of six people in a study of lie-detecting equipment, based on the idea that the stress involved in telling a lie can be measured. The results are shown in Table 10.7.5

a. Was everyone's stress level higher during a false answer than during a true answer?

Here we have to test the hypothesis that,

H0 : mu1 = mu2 Vs H1 : mu1 > mu2

where mu1 is population mean for false answer.

mu2 is population mean for true answer.

Assume alpha = level of significance = 5% = 0.05

Here sample size is small and population standard deviation is unknown so we use t-test for two sample.

First we have to check whether variances are equal or not.

Here the hypothesis is,

H0 : Variances are equal.

H1 : Variances are not equal.

This we can done by using TI-83 calculator.

steps :

STAT --> ENTER --> enter all the values in two columns --> D:2-SampFTest --> ENTER --> High light on Data --> ENTER --> List1 : select L1 --> List2 : select L2 --> Freq1:1 --> Freq2:1 --> Select alternative "not equal to"--> Calculate --> ENTER.

Test statistic F = 0.9861

P-value = 0.9881

P-value > alpha

Accept H0 at 5% level of significance.

Conclusion : Variances are equal.

Now we use pooled variances.

Ti-83 steps for two sampled t-tests are :

STAT --> TESTS --> 4:2-SampTTest --> ENTER --> --> High light on Data --> ENTER --> List1 : select L1 --> List2 : select L2 --> Freq1:1 --> Freq2:1 --> Select alternative ">"--> ENTER --> Pooled : yes --> ENTER--> Calculate --> ENTER.

Output is :

t = -0.3310

P-value = 0.3737

P-value > alpha

Accept H0 at 5% level of significance.

Conclusion : There is not sufficient evidence to say that everyone's stress level higher during a false answer than during a true answer.

b. Find the average stress levels for true and for false answers. Find the average change in stress level

Average change = 4.2/6 = 0.7

c. Find the appropriate standard error for the average difference. In particular, is this a paired or an unpaired situation?

standard error = 3.6625

This is an unpaired situation.

TRUE FALSE False-true 12.8 13.1 0.3 8.5 9.6 1.1 3.4 4.8 1.4 5 4.6 -0.4 10.1 11 0.9 11.2 12.1 0.9 total 4.2 n 6

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