Question

Bart was interested in determining if individuals talk more when nervous. He obtains 10 volunteers from undergraduate stats classes to participate in an experiment. He randomly assigns the students to one of two groups. All subjects are run separately. Subjects in the first group are told by the experimenter that in ten minutes that they will take a social IQ measure in which they will answer questions put to them by a panel of five graduate students. The conversations over the next ten minutes between the subjects and the experimenter are recorded. The experimenter responds only if directly asked a question. Subjects in the second group are told that in ten minutes they will be asked to describe how friendly they are by completing a true-false personality measure. The conversations for the next ten minutes are then recorded with the experimenter only responding to direct questions. The percent of time that each subject talked was recorded. Based on the data below, what should Bart conclude?

Social IQ Condition	Personality Measure
80	20
20	10
30	20
90	20
80	10

1. State the null and research hypotheses.

2. Find the Critical Value using the T-Table and interpret what you will do with the null hypothesis given that Critical Value

3. Identify the Correct Degrees of Freedom you’ll use in the table

4. Calculate the t-value. Show your work. Start with the formula and then plug in the correct values from there.

5. Make a decision regarding the null. Interpret your decision with regard to this question.

6. Calculate the effect size and interpret what it means.

7. Construct a 95% Confidence Interval for the difference between the two groups.

8. Reflect on the results and the exercise (summarize the results).

Answer 1

Independent samples t-test with unequal variances:

1.

Null Hypothesis(H0):

Individuals do not talk more when nervous. The mean for Social IQ Condition is not significantly greater than that of Personality Measure (The difference between the population means is not significantly greater than 0).

Research Hypothesis(H1):

Individuals talk more when nervous. The mean for Social IQ Condition is significantly greater than that of Personality Measure (The difference between the population means is significantly greater than 0).

(right-tailed test).

( =Population mean for Social IQ Condition; =Population mean for Personality Measure).

2.

Degrees of freedom, df =4

Let the Significance level, =0.05

Right-tailed test.

So, the critical value of t is t_crit =2.1318

If the test statistic, t > t_crit, reject the null hypothesis. Otherwise, do not reject the null hypothesis.

3.

Correct degrees of freedom, df =4

Let Social IQ Condition =1 and Personality Measure =2

The formula to calculate df is:

(where, sample size, n1 =n2 =5;

Sample variance 1 =s1² = =1,049.76;

Sample variance 2 =s2² =​​​​​​ =30.0304).

4.

Test statistic, t-value =2.9938

Formula to calculate t-value:

t = =2.9938

(where, =sample mean 1 =60; =sample mean 2 =16; n1 =n2 =sample size =5; s1 =std.deviation 1 =32.40; s2 =std.deviation 2 =5.48).

5.

Decision regarding the null:

Since t-value of 2.9938 > t_crit of 2.1318, reject the null hypothesis(H0) at 0.05 significance level.

Interpretation:

There is a sufficient evidence to claim that the mean for Social IQ Condition is significantly greater than that of Personality Measure, i.e., we have sufficient evidence to claim that the individuals talk more when nervous.

6.

Effect size =Cohen's d = (60-16)/23.235645 =1.8936

Formula used: d =difference in means/pooled SD

Pooled std.deviation(SD) =

Interpretation:

The effect size of 1.8936 is large which means that the difference between means is not trivial but it is of most importance.

7.

​​​​​95% Confidence Interval for the difference between the two groups =(3.19, 84.81)

8.

The 95% confidence interval for the difference in population means does not contain 0 and all values of the interval are positive, i.e., >0 which indicates that the difference is significantly greater than 0 which is supported by the conclusion of the above t-test which is again supported by the large effect size calculated above.

Thus, we have significant evidence to claim that the individuals talk more when nervous.