We considered the differences between the temperature readings in January 1 of 1

Question

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. a degrees(please round to two decimal places a degreesiplease round to two decimal places) lower bound: upper bound: (b) Interpret this interval in context. 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 90% of the time the differences in temperatures from year to year will be : between the lower bound 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 o we are 90% confident that the true meandifference 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. Yes, because the confidence interval contains mostly positive numbers No, because the confidence interval contains 0 Yes, because the confidence interval contains negative numbers No, because the confidence interval is not very wide Box 1: Enter your answer as an integer or decimal number. Examples: 3, 4, 5.5172 Enter DNE for Does Not Exist, oo for Infinity Box 2: Enter your answer as an integer or decimal number. Examples: 3, 4, 5.5172 Enter DNE for Does Not Exist, oo for Infinity Box 3: Select the best answer Box 4: Select the best answer

Explanation / Answer

Solution:- Given that mean = 1.1, standard deviation = 4.9, n = 51

t = 1.68

(a) 90% confidence interval for the average difference between = X +/- t*s/sqrt(n)
= 1.1 +/- 1.68*4.9/sqrt(51)
= -0.05 , 2.25

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