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Suppose you run a non-for-profit organization focused to keeping national parks free of litter. Crucial to getting donations to your non-for-profit is email advertising. One way to measure the success of your email advertising is to measure the amount of money coming from links to donate on your emails. Normally, your emails contain only words and numbers about litter in national parks. You believe that including images of littered areas of national parks might increase the amount in donations that you get through emails. To test if this is true, you randomly assign 50 individuals to receive the new email format with images and 42 to receive your usual email format (this is called an A/B test). The new email format had an average donation per recipient of $5.50 with a standard deviation of $2.75 while the old email format had an average donation per recipient of $3.50 with a standard deviation of $2.50. Does the average donation differ between the new and old email formats? Let µ1 be the true mean donations per recipient the for new email format and 42 be the true mean donations per recipient for the old email format. Test this hypothesis at the a = 0.01 level. (a) Set up the null and alternative hypothesis (using mathematical notation/numbers AND interpret them in context of the problem)

Suppose you run a non-for-profit organization focused to keeping national parks free of litter. Crucial to getting donations to your non-for-profit is email advertising. One way to measure the success of your email advertising is to measure the amount of money coming from links to donate on your emails. Normally, your emails contain only words and numbers about litter in national parks. You believe that including images of littered areas of national parks might increase the amount in donations that you get through emails. To test if this is true, you randomly assign 50 individuals to receive the new email format with images and 42 to receive your usual email format (this is called an A/B test). The new email format had an average donation per recipient of $5.50 with a standard deviation of $2.75 while the old email format had an average donation per recipient of $3.50 with a standard deviation of $2.50. Does the average donation differ between the new and old email formats? Let µ1 be the true mean donations per recipient the for new email format and 42 be the true mean donations per recipient for the old email format. Test this hypothesis at the a = 0.01 level. (a) Set up the null and alternative hypothesis (using mathematical notation/numbers AND interpret them in context of the problem)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Suppose you run a non-for-profit organization focused to keeping national parks free of litter. Crucial to getting donations to your non-for-profit is email advertising. One way to measure the success of your email advertising is to measure the amount of money coming from links to donate on your emails. Normally, your emails contain only words and numbers about litter in national parks. You believe that including images of littered areas of national parks might increase the amount in donations that you get through emails. To test if this is true, you randomly assign 50 individuals to receive the new email format with images and 42 to receive your usual email format (this is called an A/B test). The new email format had an average donation per recipient of $5.50 with a standard deviation of $2.75 while the old email format had an average donation per recipient of $3.50 with a standard deviation of $2.50. Does the average donation differ between the new and old email formats? Let µi be the true mean donations per recipient the for new email format and 42 be the true mean donations per recipient for the old email format. Test this hypothesis at the a = 0.01 level. (a) Set up the null and alternative hypothesis (using mathematical notation/numbers AND interpret them in context of the problem) (b) Calculate the test statistic (c) Calculate the critical value (d) Draw a picture of the distribution of the test statistic under Ho. Label and provide values for the critical value and the test statistic, and shade the critical region. (e) Make and justify a statistical decision at the a = 0.01 level and state your conclusions in context of the problem. (f) Construct a 95% confidence interval for the true difference in test scores between the two kinds of training methods. (g) Does this interval reaffirm your statistical decision from the hypothesis test? Explain.
Transcribed Image Text:Suppose you run a non-for-profit organization focused to keeping national parks free of litter. Crucial to getting donations to your non-for-profit is email advertising. One way to measure the success of your email advertising is to measure the amount of money coming from links to donate on your emails. Normally, your emails contain only words and numbers about litter in national parks. You believe that including images of littered areas of national parks might increase the amount in donations that you get through emails. To test if this is true, you randomly assign 50 individuals to receive the new email format with images and 42 to receive your usual email format (this is called an A/B test). The new email format had an average donation per recipient of $5.50 with a standard deviation of $2.75 while the old email format had an average donation per recipient of $3.50 with a standard deviation of $2.50. Does the average donation differ between the new and old email formats? Let µi be the true mean donations per recipient the for new email format and 42 be the true mean donations per recipient for the old email format. Test this hypothesis at the a = 0.01 level. (a) Set up the null and alternative hypothesis (using mathematical notation/numbers AND interpret them in context of the problem) (b) Calculate the test statistic (c) Calculate the critical value (d) Draw a picture of the distribution of the test statistic under Ho. Label and provide values for the critical value and the test statistic, and shade the critical region. (e) Make and justify a statistical decision at the a = 0.01 level and state your conclusions in context of the problem. (f) Construct a 95% confidence interval for the true difference in test scores between the two kinds of training methods. (g) Does this interval reaffirm your statistical decision from the hypothesis test? Explain.
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