Question A political campaign is considering sending a letter requesting donations to all of the tens of thousands of people on its mailing list. The campaign will only send the letter to everyone on the list if it is convinced that more than 4% of recipients will respond with donations. The campaign sends the letter to a random sample of 500 people on its list and receives donations in response from 24 recipients. At the 5% level of significance, does the campaign have convincing evidence that more than 4% of recipients on its entire mailing list will respond with donations? Identify the p-value for the appropriate hypothesis test. Round your answer to three decimal places as needed. You may use technology or the z-table below. z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.7 0.758 0.761 0.764 0.767 0.770 0.773 0.776 0.779 0.782 0.785 0.8 0.788 0.791 0.794 0.797 0.800 0.802 0.805 0.808 0.811 0.813 0.9 0.816 0.819 0.821 0.824 0.826 0.829 0.831 0.834 0.836 0.839 1.0 0.841 0.844 0.846 0.848 0.851 0.853 0.855 0.858 0.860 0.862 1.1 0.864 0.867 0.869 0.871 0.873 0.875 0.877 0.879 0.881 0.883
Added by Mar M.
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The null hypothesis (H0) is that the proportion of recipients who will respond with donations is less than or equal to 4% (p ≤ 0.04). The alternative hypothesis (H1) is that the proportion of recipients who will respond with donations is greater than 4% (p > Show more…
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Some fundraisers believe that people are more likely to make a donation if there is a relatively quick deadline given for making the donation. The paper "Now or Never! The Effect of Deadlines on Charitable Giving: Evidence from Two Natural Field Experiments" describes an experiment to investigate the influence of deadlines. In this experiment, 1.2% of those who received an email request for a donation that had a three-day deadline to make a donation and 0.8% of those who received the same email request but without a deadline made a donation. The people who received the email request were randomly assigned to one of the two groups (email with deadline and email without deadline). Suppose that the given percentages are based on sample sizes of 1,500 (the actual sample sizes in the experiment were much larger). Use a 90% confidence interval to estimate the difference in the proportion who donate for the two different treatments. (Use p_with - p_without. Use a table or SALT. Round your answers to four decimal places.
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