The image presents a dataset of paired values $x_i$ and $y_i$, along with a series of statistical problems:

1. $x_i = \{3, 12, 6, 20, 14\}$
2. $y_i = \{55, 40, 55, 10, 15\}$

The tasks include:

a. Estimating the standard deviation of $\hat{y}^*$ when $x = 8$ (to 4 decimal places).

b. Developing a 95% confidence interval for the expected value of $y$ when $x = 8$ (to 2 decimals).

c. Estimating the standard deviation of an individual value of $y$ when $x = 8$ (to 4 decimal places).

d. Developing a 95% prediction interval for $y$ when $x = 8$ (to 2 decimals).

The answers provided in the image were:

• Part a: 9.79 (incorrect)
• Part b: (12.97, 75.03) (incorrect)
• Part c: 13.115 (incorrect)
• Part d: (7.61, 80.39) (incorrect)

Would you like me to guide you through the calculations for each part and help you find the correct values?