Question

The Beautiful Body Cosmetics Company claims that its new wart cream dissolves 54% of all warts with one application. A scientist from a competing company is given the job of disproving this claim. She purchases a few jars of the product and does her own tests. This scientist tries the cream on several randomly selected people (and randomly selected warts!) and finds that after applying the cream to 300 warts, 158 of unattractive warts disappeared with one application. Perform a hypothesis test and determine what the scientist would conclude about Beautiful Body’s product.

1. State your Null Hypothesis – use words, not just a percentage.

Calculate the observed percentage and enter your answer. Round your answer to one decimal place.

Compare your observed percentage to the interval of p± 2?. Construct the proper sentence either rejecting or not rejecting the null hypothesis.

Write your conclusion in your words.

Answer 1

1) Null Hypothesis H0: p =0.54 , 54% of all warts dissolves wiith one application.

The sample proportion is

Therefore the observed percentage is = 52.7%

= ( 0.469, 0.5844)

In Percentage form = (46.9%, 58.4%)

Since the confidence interval includes the hypothetical proportion , We fail to reject the null hypothesis  

Conclusion : Scientist should enough evidence to support the Beautiful Body Cosmetics Company claims that its new wart cream dissolves 54% of all warts with one application.