Question

Independent samples t-test: An experimenter is interested in how the “foot-in-the-door” tactic could increase compliance in college students. The “foot-in-the-door” tactic involves asking first for a small request to butter someone up for a larger (originally intended) request. Typically, the “foot-in-the-door” tactic increases compliance because people do not like to appear inconsistent and since they originally agreed to the small request, they feel compelled to also agree with the large request.

Our experimenter was seeking to increase the number of students who volunteer for research in the department of psychological sciences. One group of students were subject to the “foot-in- the-door” tactic and these students were first asked to wear a sticker promoting research participation (small request) around campus. Later, these same students were asked to participate in a research project. The second group of students were simply asked to participate in research with no initial, small request.

This study was conducted across multiple semesters, and the value below represents how many students agreed to participate in research each semester.

“foot-in-the-door” (FITD): 11 8 10 6 5

Large request only (Large): 6 6 9 10 8

Now we’ll use this information for hypothesis testing....

3. What are your degrees of freedom for this independent samples t-test? 2pts.

4. What is your critical t-value (t-crit) for this hypothesis test? 2pts.

Next we calculate the t-value for our sample to compare to this critical value (see table below for reminders)......

5. What is the pooled variance for our sample? 4 pts. Pooled Variance: ??1+ ??2 =

   ?? 1+ ?? 2

6. What is the standard error of the mean difference (??1−?2)for our sample? 4 pts.

7. What is the value for t-observed? 4 pts.

8. Is there a statistically significant difference between these groups? 3pts.

Answer 1

Result:

This study was conducted across multiple semesters, and the value below represents how many students agreed to participate in research each semester.

“foot-in-the-door” (FITD): 11 8 10 6 5

Large request only (Large): 6 6 9 10 8

Now we’ll use this information for hypothesis testing....

What are your degrees of freedom for this independent samples t-test? 2pts.

?? 1+ ?? 2 =4+4=8

What is your critical t-value (t-crit) for this hypothesis test? 2pts.

At 0.05 level of significance, critical t =2.306

Next we calculate the t-value for our sample to compare to this critical value (see table below for reminders)......

What is the pooled variance for our sample? 4 pts.

Pooled Variance: ??1+ ??2 = 4.8500

What is the standard error of the mean difference (??1−?2)for our sample? 4 pts.

standard error of the mean difference = 1.3928

What is the value for t-observed? 4 pts.

t observed = 0.1436

Is there a statistically significant difference between these groups? 3pts.

Since the t observed value 0.1436 is less than the t critical value 2.306, there is no statistically significant difference between these groups.

Pooled-Variance t Test for the Difference Between Two Means
(assumes equal population variances)
Data
Hypothesized Difference	0
Level of Significance	0.05
FITD 1 Sample
Sample Size	5
Sample Mean	8
Sample Standard Deviation	2.5495
Large 2 Sample
Sample Size	5
Sample Mean	7.8
Sample Standard Deviation	1.7889
Intermediate Calculations
FITD 1 Sample Degrees of Freedom	4
Large 2 Sample Degrees of Freedom	4
Total Degrees of Freedom	8
Pooled Variance	4.8500
Standard Error	1.3928
Difference in Sample Means	0.2000
t Test Statistic	0.1436
Two-Tail Test
Lower Critical Value	-2.3060
Upper Critical Value	2.3060
p-Value	0.8894
Do not reject the null hypothesis