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%.

A market sells potatoes whose weights are normally distributed with mean 65 grams and standard deviation 15 grams.

(i) Find the probability that a randomly chosen potato weighs between 40 grams and 80 grams.
The market sells potatoes weighing more than 80 grams separately packaged. Potatoes weighing between 80 grams and L grams are labeled large and potatoes weighing over L grams are labeled as extra-large.
(ii) Given that a randomly chosen potato is twice as likely to be large as extra-large, calculate the value of L. A market sells potatoes whose weights are normally distributed with mean 65 grams and standard deviation 15 grams.

i) 0.7937

ii) .8

i want thecomplete solution

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 what the p-value suggests about the effectiveness of the DVD, we need to consider the concept of the p-value in hypothesis testing. In hypothesis testing, the null hypothesis assumes that there is no difference or no effect, while the alternative hypothesis assumes that there is a difference or an effect. The p-value is a measure of the evidence against the null hypothesis.

A low p-value indicates that there is strong evidence against the null hypothesis. In this case, the p-value of 0.003 suggests that there is a very low probability of observing the data if the null hypothesis (DVD is not more effective than sending a letter) is true.

However, it is important to note that the significance level or threshold for the p-value must be determined in advance. If the threshold is set at 0.05, for example, the p-value of 0.003 would be lower than the threshold and would lead us to reject the null hypothesis. But if the threshold is set at a lower value, such as 0.001, the p-value would not be lower than the threshold and we would fail to reject the null hypothesis.

Therefore, the correct interpretation of the p-value in this case is that it is low, but it is not conclusive evidence to conclude that the DVD is more effective than sending a letter.

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%.

To make a more informed decision about the effectiveness of the DVD, additional information such as a confidence interval would be helpful. A confidence interval provides a range of values within which the true population parameter (in this case, the proportion of delinquent customers who pay after getting the DVD) is likely to fall.

By calculating a confidence interval, we can estimate the range of effectiveness for the DVD. If the confidence interval is narrow and entirely above a certain threshold, such as 30%, we can have more confidence in concluding that the DVD is more effective than sending a letter.

Without a confidence interval, we can only state that the proportion of delinquent customers who pay after getting the DVD is greater than 30% based on the p-value. However, we cannot determine the specific range of effectiveness, which could provide more useful information for decision-making.