The dataset Climate contains information on the temperatures observed in 1948 and 2018 for a set of 197 randomly sampled locations from the National Oceanic and Atmospheric Administration's records'. In the dataset, the variable "dx90_1948" indicates the numbers of days in which the temperature exceeded 90 F in 1948 for each location. Similarly, "dx90_2018" indicates the number of days in which the temperature exceeded 90 F in 2018. We would like to determine whether the dataset provides convincing evidence that there were more days in 2018 with temperature exceeding 90 F than in 1948. To this end, answer the following questions: a) Are the observations of the number of days in which the temperature exceeded 90 F in 1948 and 2018 independent? Is there a relationship between these two datasets? Briefly explain your answer. b) Compute the difference in the number of days exceeding 90 F for each station (number of days in 2018 minus number of days in 1948). Is the distribution of the differences reasonably normal? Justify your answer. c) Use software to find the mean and the standard deviation of the differences, and then manually test the hypothesis that there were more days in 2018 with temperature exceeding 90 F than in 1948. Use a 5% significance level and the p-value approach. Confirm your results using statistical software. d) Construct manually the corresponding one-sided 95% confidence interval for the mean difference in the number of days exceeding 90 F and confirm your calculations using statistical software. Does the confidence interval confirm the conclusion obtained from the hypothesis test in part c)? Briefly explain your answer. e) Are the required conditions for the hypothesis test and confidence interval above satisfied? Briefly explain your