Activity 31

MATH 216: Statistical Thinking

Activity 1: Economy

Context: A public polling agency claims that 30% of Florida consumers are optimistic about the economy. To test this, a researcher surveys 200 people and finds only 50 optimists.

  1. Calculate the test statistic \(z_c\) for \(H_0: p = 0.3\).
  2. Determine if \(H_0\) is rejected at \(\alpha = 0.05\).

Activity 2: Confidence Interval Exploration

Context: The Bureau of Economic and Business Research (BEBR) surveys 484 consumers; 157 are optimistic about Florida’s economy.

Dataset: n = 484, optimistic count = 157.

  1. Visualize the sampling distribution with a histogram and normal curve.

Interpretation:

Activity 3: Quality Control Hypothesis Test

Context: A battery manufacturer claims fewer than 5% of its products are defective. In a batch of 300 batteries, 10 are defective.

Dataset: n = 300, defective count = 10.

  1. Calculate \(\hat{p}\) for defective batteries.
  1. Test if \(p < 0.05\) at \(\alpha = 0.05\).

Activity 4: Healthcare Hypothesis Test

Context: A hospital claims that 15% of patients experience side effects from a new medication. A researcher surveys 180 patients and finds 33 with side effects.

  1. Calculate the test statistic \(z_c\) for \(H_0: p = 0.15\).
  2. Determine if \(H_0\) is rejected at \(\alpha = 0.05\)

Activity 5: Sample Size Determination Case Study

Context: A cell phone manufacturer needs to estimate the defect rate to within 1% with 90% confidence. No prior data exists.

Tasks:

  1. Calculate the required sample size using the conservative \(p = 0.5\).

  2. Explain why \(p = 0.5\) is used when \(\hat{p}\) is unknown.

Determine sample size to estimate defective cell phones within 0.01 (90% CI).

\[ n = \frac{z_{\alpha/2}^2 \cdot p(1-p)}{SE^2} \]

Activity 6: Customer Satisfaction Confidence Interval

Context: A restaurant chain surveys 400 customers; 220 report satisfaction with their service.

Dataset: n = 400, satisfied count = 220.

  1. Calculate a 95% confidence interval for the true satisfaction proportion.
  2. Visualize the sampling distribution (histogram + normal curve).

Interpretation: