Activity 28

MATH 216: Statistical Thinking

Activity 1: Quiz

• Question: Given the null hypothesis \(H_0: \mu_{\text{A}} = \mu_{\text{B}}\) and the alternative hypothesis \(H_a: \mu_{\text{A}} > \mu_{\text{B}}\), what does rejecting \(H_0\) imply about the effectiveness of Method A compared to Method B?
• Options:
  • 1. Method A is less effective than Method B.
  • 2. Method A is equally effective as Method B.
  • 3. Method A is more effective than Method B.
  • 4. The test is inconclusive.

Activity 2: Case Studies and Problem-Solving

• Case Study: An experiment is conducted to compare the starting salaries of male and female college graduates who find jobs. Pairs are formed by choosing a male and a female with the same major and similar GPAs. The data is provided in the table below. Use \(\alpha=0.05\) to perform a hypothesis test to see if the data provide sufficient evidence to support the claim that “the male average starting salary is greater than the female average starting salary.”

Pair	Male	Female	Difference Male - Female
1	29,300	28,800	500
2	41,500	41,600	-100
3	40,400	39,800	600
4	38,500	38,500	0
5	43,500	42,600	900
6	37,800	38,000	-200
7	69,500	69,200	300
8	41,200	40,100	1,100
9	38,400	38,200	200
10	59,200	58,500	700

1. Analyze: Perform a paired t-test on the salary data.
2. Interpret: Discuss the results, including the p-value and confidence interval.
3. Conclude: Determine whether the data supports the claim that male graduates earn more than female graduates.

Activity 3: Exam Improvement

A teacher gives a pre-test and post-test to 8 students. Did scores improve? Test with α=0.05.

Data:

1. Run the paired t-test:

2. Report the p-value. Is the improvement significant?

Activity 4: Drug Effectiveness

A drug claims to reduce blood pressure. Test with α=0.05 using this data from 6 patients (mmHg):

Data:

Steps:

1. Verify normality of differences:

2. Run the test:

3. Output: