Activity 20
MATH 216: Statistical Thinking
Activity 2: Quiz
- Question: Given a sample mean \(\bar{x} = 2.283\), sample standard deviation \(s = 0.950\), and sample size \(n = 6\), calculate the t-statistic for a population mean \(\mu = 2.0\).
Activity 3: Interactive Data Exploration
Prompt: Provide students with the following dataset and ask them to explore it using RStudio:
- Task: Calculate the sample mean \(\bar{x}\) and sample standard deviation \(s\).
- Visualization: Create a histogram of the data and overlay a normal distribution curve.
Activity 4: Group Activities with Real Data
- Dataset:
- Task: Calculate the 99% confidence interval for the mean number of characters printed before the printhead fails.
- Interpretation: Discuss the implications of the confidence interval in the context of the problem.
Activity 5: Case Studies and Problem-Solving
- Scenario: A pharmaceutical company wants to estimate the mean increase in blood pressure for patients taking a new drug. They have a small sample of 6 patients with the following blood pressure increases (in points):
- Task: Construct a 95% confidence interval for the mean increase in blood pressure. Discuss the assumptions required for this interval to be valid and whether they are reasonably satisfied.
Activity 6: Calculating Sample Size
Consider a large hospital that wants to estimate the average length of stay of its patients, \(\mu\) . The hospital randomly samples \(n=100\) of its patients and finds that the sample mean length of stay is \(\bar{x}=4.5\) days. Also, suppose it is known that the standard deviation of the length of stay for all hospital patients is \(\sigma=4\) days.
Initial 95% C.I.: \(4.5 \pm 0.78\) days; width \(=1.56\) days.
Adjusting Sample Size for Precision
- Goal: Narrow C.I. width from 1.56 days to 0.50 day.
- Calculation leads to a required sample size of approximately ____ patients.