A sample of 250 adults tried the new multigrain cereal "Wow!" A total of 187 rated it as excellent. In a sample of 100 children, 66 rated it as excellent. Using the 0.1 significance level, the researcher wishes to show that adults like the cereal better than children. Which of the following is the alternate hypothesis? A) H₁: π_A = π_C B) H₁: π_A π_C D) H₁: π_A ≠ π_C

Question

A sample of 250 adults tried the new multigrain cereal "Wow!" A total of 187 rated it as excellent. In a sample of 100 children, 66 rated it as excellent. Using the 0.1 significance level, the researcher wishes to show that adults like the cereal better than children. Which of the following is the alternate hypothesis? A) H₁: π_A = π_C B) H₁: π_A < π_C C) H₁: π_A > π_C D) H₁: π_A ≠ π_C

Quizplus · Accepted Answer

The hypothesis should state that adults like the cereal better than children, which means that the proportion of adults who rate it as excellent is greater than the proportion of children who rate it as excellent. Therefore, the alternate hypothesis should be one-tailed and state that πA > πC, where πA is the true proportion of adults who rate the cereal as excellent and πC is the true proportion of children who rate the cereal as excellent. Option C is the only one-tailed hypothesis that fits this requirement.

A Sample of 250 Adults Tried the New Multigrain Cereal