A beverage company claims that on average, customers consume 500 mL of their new energy drink in a single sitting. To test this claim, a market researcher collects a random sample of 8 customers. Assume the sample is normal & make a 90% conf. int. for the true mean volume. Does the data support the company’s claim?

• A. Yes
• B. No
• C. More Information is required

Answer: (B)

Verified step by step guidance

1. Step 1: Calculate the sample mean (x̄) using the provided data. Add all the values in the table (480, 495, 470, 490, 505, 475, 460, 495) and divide by the number of observations (n = 8). Formula: x̄ = (Σx) / n.
2. Step 2: Calculate the sample standard deviation (s). Use the formula: s = sqrt(Σ(xi - x̄)^2 / (n - 1)), where xi represents each individual data point, x̄ is the sample mean, and n is the sample size.
3. Step 3: Determine the critical t-value for a 90% confidence interval with degrees of freedom (df = n - 1 = 7). Use a t-distribution table or statistical software to find the t-value corresponding to a 90% confidence level and df = 7.
4. Step 4: Calculate the margin of error (ME) using the formula: ME = t * (s / sqrt(n)), where t is the critical t-value, s is the sample standard deviation, and n is the sample size.
5. Step 5: Construct the confidence interval using the formula: CI = x̄ ± ME. Compare the interval to the company's claim of 500 mL to determine if the claim is supported.