Question

A​ company's old antihistamine formula provided relief for 68​% of the people who used it. The company tests a new formula to see if it is​ better, and gets a​ P-value of 0.29. State the null and alternative hypotheses. Is it reasonable to conclude that the new formula and the old one are equally​ effective? Explain. What is the null​ hypothesis? Upper H 0 : ▼ p ModifyingAbove p with caret y overbar mu ▼ not equals less than less than or equals greater than or equals greater than equals ▼ 29 71 0.68 0.29 What is the alternative​ hypothesis? Upper H Subscript Upper A Baseline : ▼ p y overbar mu ModifyingAbove p with caret ▼ equals greater than or equals greater than less than less than or equals not equals ▼ 29 71 0.68 0.29 Choose the correct answer below. A. Since the​ P-value is greater than ​0.05, it seems that the new formula is more effective than the old one. B. It is not reasonable to conclude that the new formula and the old one are equally effective. There is a 29​% chance the new formula is better than the old one. C. It is not reasonable to conclude that the new formula and the old one are equally effective. The​ P-value cannot suggest this conclusion. D. Since the​ P-value is greater than ​0.05, it seems that the new formula is equally effective as the old one. Click to select your answer.

Answer 1

Solution:

Given: A​ company's old antihistamine formula provided relief for 68​% of the people who used it.

Thus p = 0.68

P-value = 0.29

Part a)  State the null and alternative hypotheses.

What is the null​ hypothesis?

Since we have to test for proportion of people who used antihistamine formula provided relief, we use proportion symbol in stating hypothesis. Thus we get:

What is the alternative​ hypothesis?

Since we have to test if a new formula is​ better, this is right tailed test, thus H_A is:

Part b) Is it reasonable to conclude that the new formula and the old one are equally​ effective? Explain.

Since P-value = 0.29 > 0.05 significance level, we do not reject null hypothesis H0.

Thus it is reasonable to conclude that the new formula and the old one are equally​ effective.

Thus correct answer is:

D. Since the​ P-value is greater than ​0.05, it seems that the new formula is equally effective as the old one.