7.21 Global warming, Part II. We considered the change in the number of days exceeding 90°F from 1948 and 2018 at 197 randomly sampled locations from the NOAA database in Exercise 7.19. The mean and standard deviation of the reported differences are 2.9 days and 17.2 days.
(a) Calculate a 90% confidence interval for the average difference between number of days exceeding 90°F between 1948 and 2018. We’ve already checked the conditions for you.
(b) Interpret the interval in context.
(c) Does the confidence interval provide convincing evidence that there were more days exceeding 90°F in 2018 than in 1948 at NOAA stations? Explain
(a)
# Given data: the NOAA database in Exercise 7.19
n <- 197
df <- n -1
mean_1 <- 2.9
std_1 <- 17.2
# se, me
se <- std_1 / sqrt(n)
t_star <- abs(qt(0.05, df))
me <- t_star * se
# Confidence interval
lower_ci <- mean_1 - me
upper_ci <- mean_1 + me
ci <- c(lower_ci, upper_ci)
ci## [1] 0.8747428 4.925257290% confidence interval is (0.87, 4.93).
(b)
We are 90% confident that there was an increase of 0.87 to 4.93 in the average number of days that hit 90°F in 2018 relative to 1948 for NOAA stations.
(c)
Yes, the confidence interval provides convincing evidence that there were more days exceeding 90°F in 2018 than in 1948 at NOAA stations since the interval lies entirely above 0.