From the image, I see that you're working with a statistical analysis of the cost difference between private and public colleges. Based on your provided data:

1. Sample Mean ($\bar{x}$) and Standard Deviation ($s$): These values were computed as follows:

   • Private Colleges: $\bar{x}_1 = 42.50$, $s_1 = 6.98$
   • Public Colleges: $\bar{x}_2 = 22.30$, $s_2 = 4.53$

2. Point Estimate of the Difference Between Means:

   • $\bar{x}_1 - \bar{x}_2 = 42.50 - 22.30 = 20.20$
   • This means, on average, private colleges cost $20,200 more than public colleges annually.

3. 95% Confidence Interval for the Difference Between the Means:

   • The range provided indicates that the annual mean cost of private colleges is between $15,410 and $24,990 more than that of public colleges.

Let me know if you'd like detailed steps on how these values were computed or any specific aspect clarified further.

Here are 5 related questions to deepen your understanding:

1. What statistical formula is used to compute a confidence interval for the difference between two means?
2. How does the sample size influence the width of a confidence interval?
3. Why is it necessary to use the standard error when calculating the confidence interval?
4. How can we interpret overlapping confidence intervals for two groups?
5. What assumptions must be met to calculate this confidence interval?

Tip: Always double-check your degrees of freedom and rounding when interpreting confidence intervals to ensure accuracy in your results.