A simple regression has correlation coefficient: r = −0.118 What is R²?

A production analyst tests part strength using 4 material types and 3 curing temperatures, with repeated observations in every material/temperature cell. Excel gives: Interaction p-value = 0.276Material p-value = 0.004Temperature p-value = 0.119α = 0.05 Which conclusion is correct?

The complement of the event “at least one selected person tests positive” is “__________ selected people test positive.”

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)