Question

Can We Lessen Side Effects? – A particular pharmaceutical product causes adverse events (or side effects, such as headaches, dizziness, stomach aches) in about 15% of all patients. Hopefully, a new enteric-coated formulation should lessen that side effect rate. The company decides to use a 5% level of significance and will conduct an experiment with 200 patients.

Question 7 Subquestions

7.a Which one is the correct formulation of the null hypothesis and the alternative hypothesis for this study?

• H₀: p = 0.15 vs. H_A: p < 0.15

• H₀: p̂ = 0.15 vs. H_A: p̂ < 0.15

• H₀: p = 0.15 vs. H_A: p > 0.15

• H₀: p̂ = 0.15 vs. H_A: p̂ > 0.15

• H₀: p = 0.15 vs. H_A: p ≠ 0.15

• H₀: p̂ = 0.15 vs. H_A: p̂ ≠ 0.15

7.b Of the 200 participants, 24 developed side effects. Assuming that the new enteric-coated formulation does not lessen that side effect and the true rate for the new formulation is the same 15% as for the old pharmaceutical product, how many null-standard deviations is the observed sample proportion 24/200 from the hypothesised population proportion of 0.15?

• 1.1882 null-standard deviations above the hypothesized population proportion of 0.15

• 1.1882 null-standard deviations below the hypothesized population proportion of 0.15

• 1.3056 null-standard deviations above the hypothesized population proportion of 0.15

• 1.3056 null-standard deviations below the hypothesized population proportion of 0.15

7.c The corresponding p-value is 0.1174. Which is the appropriate conclusion at the 5% level?

• There is sufficient evidence to suggest that the population proportion of all patients taking the new formulation who experience side effects is less than 0.15.

• There is insufficient evidence to suggest that the population proportion of all patients taking the new formulation who experience side effects is less than 0.15.

Answer 1

7a)

H₀: p = 0.15 vs. H_A: p < 0.15

7b)1.1882 null-standard deviations below the hypothesized population proportion of 0.15

7c) There is insufficient evidence to suggest that the population proportion of all patients taking the new formulation who experience side effects is less than 0.15.