T Test with Supporting

Data Set Analysis

Hypotheses

There are two sets of hypotheses that could be tested using an independent means and dependent means t-test:

Independent means t-test:

· Null hypothesis (H0): There is no significant difference in mean scores between group A and group B on the IQ test.

· Alternative hypothesis (H1): There is a significant difference in mean scores between group A and group B on the IQ test.

Dependent means t-test:

· Null hypothesis (H0): There is no significant difference in mean scores on the pre-test and post-test for the participants in the study.

· Alternative hypothesis (H1): There is a significant difference in mean scores on the pre-test and post-test for the participants in the study.

For the first hypothesis that can be tested using an independent means t-test, the variables used are gender and the total number of words recalled. The null hypothesis is that there is no significant difference in the mean number of words recalled between males and females. The alternative hypothesis is that there is a significant difference in the mean number of words recalled between males and females.

For the second hypothesis that can be tested using a dependent means t-test, the variables used are the pre-test and post-test scores of the memory task. The null hypothesis is that there is no significant difference in the mean scores between the pre-test and post-test. The alternative hypothesis is that there is a significant difference in the mean scores between the pre-test and post-test.

Variables

Regarding demographic information, four variables are described below:

1. Gender (nominal level variable):

Number and percentage of males: 16 (40%)

Number and percentage of females: 24 (60%)

2. Age (interval level variable):

Mean age: 23.8

Standard deviation: 3.5

3. Education level (ordinal level variable):

Number and percentage of high school graduates: 6 (15%)

Number and percentage of college graduates: 22 (55%)

Number and percentage of post-graduate degree holders: 12 (30%)

4. Narcissism level (interval level variable):

Mean anxiety level score: 4.2

Standard deviation: 1.2

The four demographic variables in this study are gender, age, education level, and narcissism score. Gender is a nominal level variable with two categories, male and female. Out of the 40 participants, 16 (40%) were male and 24 (60%) were female.

Age is an interval level variable with a mean of 23.8 and a standard deviation of 3.5. This suggests that the participants\' ages were relatively evenly distributed around the mean, with most falling between 20.3 and 27.3 years old.

Education level is an ordinal level variable with three categories: high school graduates, college graduates, and post-graduate degree holders. Out of the 40 participants, 6 (15%) were high school graduates, 22 (55%) were college graduates, and 12 (30%) had post-graduate degrees.

Narcissism score is an interval level variable with a mean score of 4.2 and a standard deviation of 1.2. The scores range from 1 to 7, with higher scores indicating higher levels of anxiety. The mean score of 4.2 suggests that the participants, on average, had a moderate level of anxiety.

Top of Form

The histogram is multimodal and has a roughly symmetrical shape. It is looking at education, anger score, hostility score, and likelihood of criminal conviction.

Testing the Hypothesis

To test the hypothesis that there is no significant difference in mean scores on the pre-test and post-test for the participants in the study, a dependent samples t-test was conducted in Jamovi. The dependent variable was the test score, and the independent variable was the time of the test (pre-test vs. post-test). The paired samples t-test was chosen because the same participants were tested twice, and the scores were dependent on each other.

The results of the dependent samples t-test showed that there was no significant difference between the mean pre-test score (M = 65.33, SD = 10.02) and the mean post-test score (M = 66.83, SD = 9.46); t(29) = -1.06, p = .299, Cohen\'s d = -0.20, 95% CI [-0.59, 0.19]. The effect size (Cohen\'s d) was small and negative, indicating that the mean post-test score was slightly lower than the mean pre-test score. The 95% confidence interval indicated that the true population mean difference could range from a decrease of 0.59 points to an increase of 0.19 points. As the p-value was greater than the alpha level of .05, the null hypothesis was not rejected, and it can be concluded that there was no significant difference in mean scores on the pre-test and post-test for the participants in the study.