Suppose that Max is a climate change scientist and butterfly enthusiast. In Max's locale, the mean summer temperature over the last ten years was higher than it was in the previous ten years. Max wonders if the size of adult male monarch butterflies has changed with the temperature difference. He knows that in his locale, historically, the mean rear wing length of adult male monarchs was 37.4 mm. He collects a random sample of n adult male monarchs to compare to the historical average. His sample data is shown in the given stem-and-leaf plot, where the stem unit is mm and the leaf unit is tenths of a mm. 6 36 6 33538 37 0 1 2 3 4 4 5 7 99 0 1 3 4 6 6 6 9 9 9 39 3 Leaf unit = 0.1 mm From experience, Max knows that the rear wing length of monarch butterflies is normally distributed. He decides to use a 1- test with a significance level of a = 0.05 to test the null hypothesis, Io: 37.4 against the alternative hypothesis, H 37.4, where u is the population mean. If the requirements for a 1-test have not been met, only state the test decision and conclusion. Otherwise, find the mean, standard deviation, 1-statistic, P-value, and state the test decision and conclusion. First, compute the mean, x, of Max's sample. Report your answer with two decimals of precision. x = mm Then, compute the sample standard deviation, s. Report your answer with two decimals of precision. mm Next, compute the 1-statistic of the test. Report your answer with three decimals of precision. Next, compute the r-statistic of the test. Report your answer with three decimals of precision. 1-statistic= Then, use software to calculate the P-value for the test. Report your answer with three decimals of precision. P-value= Finally, state the decision and conclusion of Max's test. Max decision The conclusion is that mean wing size of adult male monarch butterflies 9 the the current Answer Bank is less than 37.4 mm to reject there is insufficient evidence that there is sufficient evidence that about is different than 37.4 mm because the requirements have not been met cannot make a alternative hypothesis no conclusion can be made about to fail to reject is greater than 374 mm null hypothesis should make the is equal to 37.4 mm Suppose that Michael reads somewhere on the Internet that, on average, middle-aged people between 45 and 65 years old visit 9 different websites per day on weekend days. Michael knows that he cannot trust everything he reads on the Internet, so he decides to conduct his own study. He believes that the middle-aged people in his community visit more than 9 websites per day. He surveys a random sample of 14 middle-aged people in his community and asks them to look at their browsing history and count the number of different websites they visited last Saturday. The following stem and leaf plot shows the number of websites visited last Saturday by each person in the survey. The stem unit is tens and the leaf unit is ones. 0 4 0578999 1 2 3 4 4 1899 Leaf unit I website 12 Michael assumes that the number of websites middle-aged people visit on the weekends is normally distributed, so he decides to perform a t-test with a significance level of a=0.05 to test the null hypothesis, Ho: 9 against the alternative hypothesis. H: >9, where u is the population mean. If the requirements for a f-test have not been met, only answer the final question. Otherwise, answer all five of the following questions. First, compute the mean, x, of Michael's sample. Report your answer with two decimals of precision. x = Then, compute the sample standard deviation, s. Report your answer with two decimals of precision. Next, compute the I-statistic of the test. Report your answer with three decimals of precision. websites websites Next, compute the 1-statistic of the test. Report your answer with three decimals of precision. 1-statistic Then, use software to calculate the P-value for the test. Report your answer with three decimals of precision. P-value= Finally, use the words and descriptions below to state the decision and conclusion of Michael's test. Michael the decision The conclusion is that number of websites visited by middle-aged people on the weekends Amwer Bank null hypothesis because the requirements have not been met is less than 9 is greater than 9 about no conclusion can be made about there is insufficient evidence that to fail to reject there is sufficient evidence that is equal to 9 should make the to reject alternative hypothes cannot make a the mean