To complete this assignment and address the provided task, here's a structured approach:

Step 1: Organize and Summarize the Data

The two groups are:

• Under 25: 12, 42, 25, 23, 18, 28, 35, 37
• Over 25: 25, 12, 21, 20, 21, 30, 5, 22

Calculate the mean (average) and sum of squares (SS) for each group. The formulas are:

• Mean: $\bar{x} = \frac{\sum x}{n}$
• Sum of Squares: $SS = \sum (x - \bar{x})^2$

Step 2: State Hypotheses for a Two-Tailed t-Test

• Null Hypothesis ($H_0$): There is no significant difference in social media usage between the groups.
  $H_0: \mu_{\text{Under 25}} = \mu_{\text{Over 25}}$
• Alternative Hypothesis ($H_a$): There is a significant difference.
  $H_a: \mu_{\text{Under 25}} \neq \mu_{\text{Over 25}}$

Step 3: Perform t-Test

Use the formula for an independent samples t-test: $t = \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{\frac{SS_1}{n_1} + \frac{SS_2}{n_2}}}$ Where:

• $\bar{x}_1, \bar{x}_2$: means of the two groups
• $SS_1, SS_2$: sum of squares of the two groups
• $n_1, n_2$: sample sizes of the two groups

Step 4: Calculate Effect Size (Cohen’s d)

$d = \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{\frac{SS_1 + SS_2}{n_1 + n_2 - 2}}}$

Step 5: Draw Conclusions

Compare the calculated $t$-value to the critical $t$-value for $\alpha = 0.05$ (two-tailed). State if the null hypothesis is rejected or not and interpret the result.

Would you like me to calculate the mean, sum of squares, and conduct the t-test with this data?

Related Questions:

1. What is the difference between one-tailed and two-tailed hypothesis tests?
2. How do you interpret Cohen’s $d$ effect size?
3. Why is it important to calculate the degrees of freedom for a $t$-test?
4. What assumptions must be met for an independent samples $t$-test?
5. How do outliers impact the results of hypothesis testing?

Tip:

Always check the assumptions of the $t$-test before conducting the analysis: independence, normality, and homogeneity of variances.