Problem : A coffee shop owner claims that the average caffeine content in their new espresso blend is 120 mg per serving. A random sample of 30 servings was tested, revealing an average caffeine content of 125 mg with a standard deviation of 10 mg. Determine whether there is significant evidence to suggest the true caffeine content is different from the owner's claim. Step 1: State the Hypothesis Null Hypothesis (Ho): μ = 120 (The average caffeine content is 120 mg) Alternative Hypothesis (Ha): μ ≠ 120 (The average caffeine content is different from 120 mg) Step 2: Identify Given Values Significance level: α = 0.05 (95% confidence level) Sample size: n = 30 Sample mean: x̄ = 125 Claimed population mean: μ = 120 Standard deviation: s = 10 Step 3: Compute the t-Statistic (use t-test calculator for verification) Using the t-distribution formula: Step 4: Determine Degrees of Freedom (df) 𝑑𝑓 = 𝑛 − 1 = 30 − 1 = 29 Step 5: Find the Critical t-Value Using...