Paul owns a mobile wood-fired pizza oven operation. A couple of his clients complained about his dough at a recent catering, so he changed his dough to a newer product. Using the old dough, there were 6 complaints out of 385 pizzas. With the new dough, there were 16 complaints out of 340 pizzas. Let p₁ be the proportion of customer complaints with the old dough and p₂ be the proportion of customer complaints with the new dough. State the competing hypotheses to determine if the proportion of customer complaints using the old dough is less than the proportion of customer complaints using the new dough. A) H₀: p₁ - p₂ ≤ 0, H_A: p₁ - p₂ 0 B) H₀: p₁ - p₂ ≥ 0, H_A: p₁ - p₂ 0, H_A: p₁ - p₂ ≤ 0

Question

Paul owns a mobile wood-fired pizza oven operation. A couple of his clients complained about his dough at a recent catering, so he changed his dough to a newer product. Using the old dough, there were 6 complaints out of 385 pizzas. With the new dough, there were 16 complaints out of 340 pizzas. Let p₁ be the proportion of customer complaints with the old dough and p₂ be the proportion of customer complaints with the new dough. State the competing hypotheses to determine if the proportion of customer complaints using the old dough is less than the proportion of customer complaints using the new dough. A) H₀: p₁ - p₂ ≤ 0, H_A: p₁ - p₂ > 0 B) H₀: p₁ - p₂ ≥ 0, H_A: p₁ - p₂ < 0 C) H₀: p₁ - p₂ = 0, H_A: p₁ - p₂ ≠ 0 D) H₀: p₁ - p₂ > 0, H_A: p₁ - p₂ ≤ 0

Quizplus · Accepted Answer

We are testing if the proportion of customer complaints using the old dough is less than the proportion of customer complaints using the new dough. This is a one-sided test (less than), so we reject the null hypothesis if the difference in proportions (old-new) is statistically significant and negative. Therefore, we need to set up the null hypothesis as p₁ - p₂ ≥ 0 (or no difference or the old dough is worse) and the alternative hypothesis as p₁ - p₂ < 0 (or a negative difference or the new dough is better). Option B is the only one that has the correct inequality for the null and alternative hypotheses.

Paul Owns a Mobile Wood-Fired Pizza Oven Operation