Let's break down the matching problems and procedures based on the uploaded image:

1. Problem 1:
   "To test that a gasoline additive increases mileage..."
   The difference between mileage with and without the additive is analyzed for each car. This is a paired-data test because the same cars are used in both conditions.
   Answer: 1-tailed test of paired-data with positive critical value (Procedure 4).

2. Problem 2:
   "Test size C battery mean life is at least 25 hours."
   Testing if the mean life is at least a certain value involves a 1-tailed test for the mean.
   Answer: 1-tailed test of mean with negative critical values (Procedure 3).

3. Problem 3:
   "Run times of GotYourGP and WeTrackYou.Inc..."
   Comparing the means of two independent populations requires a 2-tailed test of means of 2 independent populations.
   Answer: 2-tailed test of means of 2 independent populations (Procedure 5).

4. Problem 4:
   "Given weights...test the population mean is 35."
   Testing if the sample mean is equal to a hypothesized population mean involves a 2-tailed test of the mean.
   Answer: 2-tailed test of mean with both negative and positive critical values (Procedure 2).

5. Problem 5:
   "An effective vaccine would reduce the proportion of exposed persons contracting a disease..."
   Testing if the proportion of vaccinated individuals who contract the disease is less than 40% involves a 1-tailed test of proportion with a negative critical value.
   Answer: 1-tailed test of proportion with negative critical value (Procedure 1).

Final Answers:

1. Problem 1 → Procedure 4
2. Problem 2 → Procedure 3
3. Problem 3 → Procedure 5
4. Problem 4 → Procedure 2
5. Problem 5 → Procedure 1

Would you like me to explain any of these matches or provide further details?

5 Follow-Up Questions:

1. What is the significance of using a 1-tailed vs. 2-tailed test in hypothesis testing?
2. Why is it important to distinguish between paired and independent data sets?
3. How do we calculate the critical value for a given alpha level?
4. What is the relationship between p-value and critical value in hypothesis testing?
5. How can sample size affect the outcome of these statistical tests?

Tip:

Always verify whether the problem involves paired samples (e.g., before-and-after measures) or independent samples, as this significantly affects the choice of statistical test.