The bank sets up an experiment to test the effectiveness of the DVD. The mail it out to a random sample of delinquent customers and keep track of how many actually do contact the bank to arrange payments. The bank's statistician calculates a p-value (probability-value) of 0.003.
1. What does this p-value suggest about the effectiveness of the DVD?
A) This is low p-value which leads us to reject the null hypothesis and conclude that the DVD is more effective than sending a letter.
B) This is low p-value which leads us to reject the null hypothesis and we cannot conclude that the DVD is more effective than sending a letter.
C) This is not a low p-value so we fail to reject the null hypothesis and conclude that the DVD is more effective than sending a letter.
D) This is not a low p-value so we reject the null hypothesis and conclude that the DVD is more effective than sending a letter.
E) The p-value is not helpful in making a decision.
2. What additional information might be helpful in making the decision about the effectiveness of the DVD?
A) The results are very clear so no additional information is needed.
B) A confidence interval would be helpful since we can only state that the proportion of delinquent customers who pay after getting the DVD is greater than 30%.
C) The bank statistician should recalculate the p-value since it is probably incorrect.
D) A confidence interval would be helpful since we can only state that the proportion of delinquent customers who pay after getting the DVD is less than 30%.
1. B) This is a low p-value which leads us to reject the null hypothesis and we cannot conclude that the DVD is more effective than sending a letter.
To understand why, we need to understand what a p-value is. In statistical hypothesis testing, the p-value is the probability of obtaining a result as extreme as, or more extreme than, the observed data, assuming that the null hypothesis is true. The null hypothesis in this case would be that there is no difference in effectiveness between sending a DVD and sending a letter.
When the p-value is low (typically below a predetermined significance level, often 0.05), it suggests that the observed data is unlikely to have occurred by chance alone, assuming the null hypothesis is true. In this case, a p-value of 0.003 indicates strong evidence against the null hypothesis, meaning that the DVD is likely more effective than sending a letter.
However, it's important to note that the p-value does not provide information about the size or practical importance of the difference. It only tells us about the likelihood of the observed data under the null hypothesis. Therefore, we cannot conclusively say that the DVD is more effective than sending a letter based solely on the p-value.
2. B) A confidence interval would be helpful since we can only state that the proportion of delinquent customers who pay after getting the DVD is greater than 30%.
A confidence interval provides a range of plausible values for the true population parameter (in this case, the proportion of delinquent customers who pay after getting the DVD). It gives us a range of values within which we can be reasonably confident that the true value lies.
In this case, knowing the confidence interval would be helpful because it would provide a more precise estimate of the proportion of customers who pay after receiving the DVD. It would give us a range of values, instead of just stating that the proportion is greater than 30%. This additional information would allow for a more informed decision-making process regarding the effectiveness of the DVD.