Question

You work for a pharmaceutical company that is testing a new cholesterol drug. The proportion of patients on the previous drug who had a positive treatment was 0.375. You want to see if the new drug is more effective than the previous drug. You conduct a sample of 113 patients on the new drug and find that 76 have had a positive treatment effect. The 95% confidence interval is ( 0.586 , 0.7591 ). What is the best conclusion you can make of those listed below?

1) The confidence interval does not provide enough information to form a conclusion.

2) The proportion of patients on the new drug who saw a positive treatment effect from 0.375 is 95%.

3) We can conclude that the proportion of patients who see a positive treatment effect with the new drug is larger than 0.375.

4) We can not claim that the proportion of patients who see a positive treatment effect with the new drug differs from 0.375.

5) We can claim that the proportion of patients who see a positive treatment effect with the new drug is smaller than 0.375.

Based on past data, the producers of Ice Mountain bottled water knew that the proportion of people who preferred Ice Mountain to tap water was 0.664. To see how consumer perception of their product has changed, they decide to conduct a survey. Of the 118 respondents, 85 indicated that they preferred Ice Mountain to the tap water in their homes. The 90% confidence interval for this proportion is ( 0.6524 , 0.7883 ). What is the best conclusion of those listed below?

1) We can conclude that the proportion of consumers who prefer Ice Mountain to their tap water is larger than 0.664.

2) The proportion of consumers who prefer Ice Mountain is 0.664 with 90% confidence.

3) The confidence interval does not provide enough information to form a conclusion.

4) We can claim that the proportion of consumers who prefer Ice Mountain to their tap water is smaller than 0.664.

5) We can not conclude that the proportion of consumers who prefer Ice Mountain to their tap water differs from 0.664.

Answer 1

1. As the proportion 0.375 is not included in the 95% confidence interval ( 0.586 , 0.7591 ) and is less than the lower limit of the interval, we can conclude that the proportion of patients who see a positive treatment effect with the new drug is larger than 0.375.

Answer: 3) We can conclude that the proportion of patients who see a positive treatment effect with the new drug is larger than 0.375.

2. As the proportion 0.664 is within the 90% confidence interval ( 0.6524 , 0.7883 ), we can not conclude that the proportion of consumers who prefer Ice Mountain to their tap water differs from 0.664.

Answer: 5) We can not conclude that the proportion of consumers who prefer Ice Mountain to their tap water differs from 0.664.