Question

1. Motivational speakers want to be perceived as trustworthy. One hypothesis is that speakers who exhibit immediacy behaviors such as making eye contact, smiling and leaning forward might be perceived as more trustworthy than those who do not engage in these behaviors. To test this hypothesis, a psychologist obtained data from 26 participants. For people in a nonimmediacy group, the speaker did not engage in any immediacy behaviors. For the immediacy group, however, the speaker made eye contact, smiled and leaned forward while giving a speech. After the speech, participants rated the speaker on a scale of trustworthiness ranging from 1 (not at all trustworthy) to 9 (highly trustworthy). The following data were obtained. Test whether the immediacy behaviors of the speaker affect trustworthiness rating.

No immediacy behavior		Immediacy behavior
4	4	7	4
5	3	6	5
3	5	9	8
4	6	8	7
6	3	8	6
7	5	7	8
7		6

1. Identify IV(s) and DV(s) of the experiment.
2. What is the researcher's question(s)?
3. State the null and alternative hypotheses
4. Compute the t-statistic.
5. Draw a conclusion by comparing the t-values (i.e., the t-obtained value and the t-critical valu.
6. The z-table provides the exact p-value for a given z-statistic. However, because the t-table does not provide the exact p-value for a given t-statistic, we will infer the approximate p-value based on the answer in 1-e. What is the approximate p-value? Also, draw a conclusion using the approximate p-value. Did you reach the same conclusion as the one you draw in 1-e?
7. Construct a 95% confidence interval and explain the meaning of the computed interval.
8. Compute the effect size.

Conceptual questions (Use the numbers that you obtained above if necessary):

1. Assume that you decide to reject the null hypothesis. Whenever you reject the null hypothesis, you commit certain amount of a Type I error. How much a Type I error approximately would you commit if you decide to reject the null? How does it differ from the alpha level that you set above?

10. Write a brief report that describes the result of this hypothesis testing. For this, you have to specify what test you applied, what was the purpose of the hypothesis testing, and what you found. Report the test value with df, the p-value, and the effect size (if you found one). Also, report the mean and SD of each group. (Read the SPSS book).
11. Which test did you apply? Why did you apply this test?

Answer 1

Solution:

a) The independent variable is behavior of motivational speakers and dependent variable is trustworthiness of motivational speakers.

b) The research question is whether the immediacy behavior of speaker affect the trustworthiness of speaker or not.

c) The null and alternative hypotheses are as follows:

  i.e. The population mean of trustworthiness ratings for the both the groups is same.

i.e. The population mean of trustworthiness ratings of no immediacy group is less than that of immediacy group.

d) To test the hypothesis we shall use two-independent samples t-test (assuming equal population variances). The test statistic is given as follows:

Where, are sample means, S^{​​​​​​2}_{​​​​​pooled} is pooled estimate of common population variance and n_{​​​​​​1}, n_{​​​​​​2} are sample sizes.

The degrees of freedom for the test is (n_{​​​​​​1} + n_{​​​​​​2} - 2).

x : No immediacy behavior, y : Immediacy behavior

n_{​​​​​​1} = 13 and n_{​​​​​​2} = 13

The value of the t statistic is -3.7442.

The degrees of freedom = 13 + 13 - 2 = 24.

e) To obtain the critical t-value, we need significance level and degrees of freedom. In our question significance level is not given. Generally significance level of 0.05 or 0.01 are used. We shall use significance level of 0.05. And we have degrees of freedom = 24.

Since, our test is left-tailed test therefore, we shall obtain left-tailed critical value. The left-tailed critical values at 0.05 significance level and 24 degrees of freedom is given as follows:

Critical value= -1.71088 (left-tailed)

For left-tailed t-test, we make decision rule as follows:

If t > left-tailed critical value, then we fail to reject the null hypothesis.

If t < left-tailed critical value, then we reject the null hypothesis.

We have, t = -3.7442 and critical value (left-tailed) = -1.71088

Since, t < left-tailed critical value, therefore we shall reject the null hypothesis at 0.05 significance level.

Conclusion: At significance level of 0.05, there is enough evidence to support the claim that the immediacy behaviors of the speaker affect trustworthiness rating.