5.21 Global warming, Part II: We considered the differences between the temperature readings in January 1 of 1968 and 2008 at 51 locations in the continental US in Exercise 5.19. The mean and standard deviation of the reported differences are 1.1 degrees and 4.9 degrees respectively. (a) Calculate a 90% confidence interval for the average difference between the temperature measurements between 1968 and 2008. lower bound: ______ degrees(please round to two decimal places) upper bound: ______ degrees(please round to two decimal places) (b) Interpret this interval in context. There is a 90% chance that the difference in temperatures in a city from year to year will be between the lower bound and upper bound We are 90% confident that 90% of the time the differences in temperatures from year to year will be between the lower bound and upper bound We are 90% confident that the true mean difference in temperatures is contained between the lower bound and upper bound We are 90% confident that the mean difference in these sample temperatures is contained between the lower bound and upper bound (c) Does the confidence interval provide convincing evidence that the temperature was higher in 2008 than in 1968 in the continental US? Explain. No, because the confidence interval contains 0 Yes, because the confidence interval contains mostly positive numbers No, because the confidence interval is not very wide Yes, because the confidence interval contains negative numbers
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Since we are not given the sample size (n), we will assume it is large enough for the Central Limit Theorem to apply. The SE is calculated as: SE = σ / √n where σ is the standard deviation of the differences (4.9 degrees) and n is the sample size. Since we don't Show more…
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We considered the differences between the temperature readings in January 1 of 1968 and 2008 at 51 locations in the continental US. The mean and standard deviation of the reported differences are 1.1 degrees and 4.9 degrees respectively. (a) Calculate a 90% confidence interval for the average difference between the temperature measurements between 1968 and 2008. lower bound: degrees(please round to two decimal places) upper bound: degrees(please round to two decimal places) (b) Interpret this interval in context. We are 90% confident that 90% of the time the differences in temperatures from year to year will be between the lower bound and upper bound There is a 90% chance that the difference in temperatures in a city from year to year will be between the lower bound and upper bound We are 90% confident that the mean difference in these sample temperatures is contained between the lower bound and upper bound We are 90% confident that the true mean difference in temperatures is contained between the lower bound and upper bound (c) Does the confidence interval provide convincing evidence that the temperature was higher in 2008 than in 1968 in the continental US? Explain. No, because the confidence interval contains 0 No, because the confidence interval is not very wide Yes, because the confidence interval contains negative numbers Yes, because the confidence interval contains mostly positive numbers
Adi S.
1. Global warming, Part I. Is there strong evidence of global warming? Let's consider a small scale example, comparing how temperatures have changed in the US from 1968 to 2008. The daily high temperature reading on January 1 was collected in 1968 and 2008 for 51 randomly selected locations in the continental US. Then the difference between the two readings (temperature in 2008 - temperature in 1968) was calculated for each of the 51 different locations. The average of these 51 values was 1.1 degrees with a standard deviation of 4.9 degrees. We are interested in determining whether these data provide strong evidence of temperature warming in the continental US. (a) Is there a relationship between the observations collected in 1968 and 2008? Or are the observations in the two groups independent? Explain. (b) Write hypotheses for this research in symbols and in words. (c) Check the conditions required to complete this test. (d) Calculate the test statistic and find the p-value. (e) What do you conclude? Interpret your conclusion in context. (f) What type of error might we have made? Explain in context what the error means. (g) Based on the results of this hypothesis test, would you expect a confidence interval for the average difference between the temperature measurements from 1968 and 2008 to include 0? Explain your reasoning.
Ariana N.
The topic of global warming increasingly appears in the news. It has the potential to impact companies' operations through changes in governmental regulations, new reporting requirements, necessary operational changes, and so on. A survey of senior finance professionals was taken to gauge members' thoughts on global warming and its impact on their companies. The survey found that 68% of senior finance professionals believe that global warming is having a significant impact on the environment. Suppose that you select a sample of 100 senior finance professionals. Complete parts (a) through (d) below: (a) What is the probability that the sample percentage indicating global warming is having a significant impact on the environment will be between 62% and 73%? 0.7592 (Type an integer or decimal rounded to four decimal places as needed) (b) The probability is 70% that the sample percentage will be contained within what symmetric limits of the population percentage? The probability is 70% that the sample percentage will be contained above 63.2% and below 72.8% (Type integers or decimals rounded to one decimal place as needed) (c) The probability is 91% that the sample percentage will be contained within what symmetrical limits of the population percentage? The probability is 91% that the sample percentage will be contained above % and below %. (Type integers or decimals rounded to one decimal place as needed)
Kari H.
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