A coffee chain claims that the mean caffeine content of its espresso shots is 63 milligrams. A health journalist selected a random sample of 18 shots and measured the caffeine content of each, obtaining a sample mean of 68.2 milligrams and a sample standard deviation of 9.5 milligrams. The journalist will carry out a two-sided t-test at the 0.05 level, for which the critical value with 17 degrees of freedom is 2.110. Which of the following gives the value of the test statistic and the correct decision?
a significance test for a population mean
Review a significance test for a population mean for AP Statistics and try 2 free AP-style practice questions. 15 questions on this topic in AP Statistics · Unit 7 · Inference for Quantitative Data: Means.
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A transit agency tests whether the mean delay of its buses differs from 0 minutes. A random sample of 45 bus trips gives a mean delay of 2.3 minutes with a standard deviation of 7.8 minutes, and the two-sided p-value is 0.054. The agency had chosen a significance level of 0.05 before collecting the data. A city council member argues, "The result is almost significant, so we should conclude that the buses run late." Is this reasoning valid?
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Answer, then see why
The price of gasoline rises 10% and the quantity demanded falls 5%. What happens to total revenue?
Not quite. The answer is B.
Why the other options are wrong
AI grading for free-response
Write your FRQ answer and get it scored point by point against the AP rubric, with the line from your answer that earned or missed each point.
Question 13 / 4 pts
Part a1 / 1 pts
Point 1: Earned
Grader confidence 94% sureReason: Correctly identifies demand for gasoline as inelastic.
Evidence: "The price of gasoline rises and the quantity falls only a little."
Part b2 / 3 pts
Point 1: Earned
Grader confidence 91% sureReason: Graph shows relatively inelastic demand.
Evidence: Draws a steep demand curve.
Point 2: Earned
Grader confidence 88% sureReason: Correct new equilibrium price.
Evidence: Shifts supply left, P1 → P2.
Point 3: Not earned
Grader confidence 82% sureReason: With inelastic demand, a price increase raises total revenue.
Evidence: "Revenue goes down."