The problem asks to calculate the point estimate for the population mean of the paired differences between two dependent random samples. Here's the approach for step 1:

Step-by-Step:

1. Paired differences (d): Use the formula $d = x_2 - x_1$, where $x_1$ and $x_2$ are the corresponding values from Population 1 and Population 2.

   For the dataThe problem asks to calculate the point estimate for the population mean of the paired differences between two dependent random samples. Here's the approach for step 1:

Step-by-Step:

1. Paired differences (d): Use the formula $d = x_2 - x_1$, where $x_1$ and $x_2$ are the corresponding values from Population 1 and Population 2.

   For the

   • Population 1: $[22, 39, 20, 34, 43, 17, 45]$
   • Population 2: $[33, 45, 35, 46, 35, 27, 37]$

   Compute the differences:

   • $d_1 = 33 - 22 = 11$
   • $d_2 = 45 - 39 = 6$
   • $d_3 = 35 - 20 = 15$
   • $d_4 = 46 - 34 = 12$
   • $d_5 = 35 - 43 = -8$
   • $d_6 = 27 - 17 = 10$
   • $d_7 = 37 - 45 = -8$

2. Mean of the differences (point estimate): Now, calculate the mean $\bar{d}$ of these differences: $\bar{d} = \frac{11 + 6 + 15 + 12 - 8 + 10 - 8}{7}$ Simplifying: $\bar{d} = \frac{38}{7} \approx 5.4$

Answer:

The point estimate for the population mean of the paired differences is approximately 5.4.

Would you like to proceed with further steps or details on this?

Here are 5 questions related to this concept:

1. How do you calculate a confidence interval for paired differences?
2. What is the significance of using a 98% confidence level in this context?
3. Why is it necessary for both populations to be normally distributed?
4. How do sample size and variability affect the confidence interval?
5. How would the process change if the populations were independent rather than dependent?

Tip: When calculating paired differences, always ensure the correct subtraction order (Population 2 minus Population 1 in this case).