A campus analyst predicts first-year GPA using placement-test score X₁ and weekly study hours X₂. Excel gives: Intercept = 0.842X₁ coefficient = 0.018X₂ coefficient = 0.064R Square = 0.731Significance F = 0.003 Which equation is correct?

A z-score of -2.45 indicates that the observed value is 2.45 standard deviations below the mean and would be considered unusual using the “more than 2 standard deviations” rule.

A textile-safety researcher collects the following independent flammability ratings from Lab A. One scheduled test was not completed, so there is one blank entry. Lab A ratings: 12.413.112.9blank13.712.514.013.212.8 What is the average rating for Lab A?

A quality analyst compares the proportion of defective items from Supplier A and Supplier B. Let p₁ = defective-item proportion for Supplier A. Let p₂ = defective-item proportion for Supplier B. The analyst claims that Supplier A and Supplier B have the same defective-item proportion. Which setup is correct?

A two-sample mean test has H₁: μ₁ ≠ μ₂ and α = 0.02. Enter the left [left]_____ and right [right]_____critical values. If there is no critical value enter “na”. (round to 3 decimals)

A security checkpoint detects an average of λ = 0.9 prohibited carry-on items per hour. Assume detections follow a Poisson distribution. Find the probability that at least 2 prohibited items are detected in a randomly selected hour. Enter your answer rounded to 3 decimal places.

A call center finds that 35% of callers ask for technical support. Assuming each call is independent, what is the probability that the next 2 callers both ask for technical support? (round to 3 decimals)

A researcher is constructing a 90% confidence interval for a population proportion. What is the positive critical value for alpha/2?

A help desk receives an average of λ = 8.4 urgent tickets per shift. Assume urgent tickets follow a Poisson distribution. Find the probability that more than 10 urgent tickets are received during a randomly selected shift. Enter your answer rounded to 3 decimal places.

A marketing researcher claims that the proportion of customers who recognize Brand A is the same as the proportion who recognize Brand B. Use the following data: α = 0.05 Brand A: n₁ = 300, x₁ = 204 Brand B: n₂ = 250, x₂ = 150 p̂₁ = 204/300 p̂₂ = 150/250 Which answer is correct?