Question

June = [62.6 63.7 65.5 60.3 64.7 61.4 63.8 65.6 65.5 60.7 67.3 64.9 65.3 65.4 70.7 62.7 59.7 68.1 63.3 68.6 66.2 68.8 67.2 63.9 66.1 62.6 64.1 57.3 67.8 67.4 66.9 64.7 64.4 65.2 68.5 66.5 64.7 65.4 65.7 62.8 59.1 66.0 65.7 60.0 67.5 69.1 73.8 64.1 66.9 70.1 61.9 63.1 68.2 71.4 67.0 68.9 63.4 66.3 62.7 65.9 69.0 65.4 62.5 68.2 68.5 69.8 63.6 63.6 66.5 66.8 69.9 67.5 67.2 67.1 68.8 67.8 70.3 67.1 ]

July = [68.8 73.0 69.3 68.6 71.2 71.5 71.2 71.3 67.9 68.5 69.7 69.9 71.8 74.5 68.0 75.3 67.3 72.2 71.4 70.4 68.8 73.6 74.0 68.5 73.8 67.9 69.6 68.3 71.8 65.0 68.3 68.2 73.6 74.2 71.7 72.2 69.5 71.9 71.8 71.1 70.9 73.5 70.6 68.9 71.5 74.0 75.8 75.8 70.0 70.2 64.3 67.0 67.6 70.0 67.8 69.2 71.7 71.5 70.6 72.5 73.0 70.4 68.2 71.3 74.9 74.0 70.3 66.5 72.0 74.5 76.6 71.7 69.4 72.5 71.9 72.1 70.9 72.2 ]

5a) What is the probability that the variance of June is different than the variance of July?

5b) What is the probability that

June 1942 - 1967 (first 26 data points) June 1968 - 1993 (next 26 data points) June 1994 - 2019 (last 26 data points)

all have the same average temeprature using an ANOVA test?

Answer 1

The R code is:

June <- c(62.6, 63.7, 65.5, 60.3, 64.7, 61.4, 63.8, 65.6, 65.5, 60.7, 67.3, 64.9, 65.3, 65.4, 70.7, 62.7, 59.7, 68.1, 63.3, 68.6, 66.2, 68.8, 67.2, 63.9, 66.1, 62.6, 64.1, 57.3, 67.8, 67.4, 66.9, 64.7, 64.4, 65.2, 68.5, 66.5, 64.7, 65.4, 65.7, 62.8, 59.1, 66.0, 65.7, 60.0, 67.5, 69.1, 73.8, 64.1, 66.9, 70.1, 61.9, 63.1, 68.2, 71.4, 67.0, 68.9, 63.4, 66.3, 62.7, 65.9, 69.0, 65.4, 62.5, 68.2, 68.5, 69.8, 63.6, 63.6, 66.5, 66.8, 69.9, 67.5, 67.2, 67.1, 68.8, 67.8, 70.3, 67.1)
July <- c(68.8, 73.0, 69.3, 68.6, 71.2, 71.5, 71.2, 71.3, 67.9, 68.5, 69.7, 69.9, 71.8, 74.5, 68.0, 75.3, 67.3, 72.2, 71.4, 70.4, 68.8, 73.6, 74.0, 68.5, 73.8, 67.9, 69.6, 68.3, 71.8, 65.0, 68.3, 68.2, 73.6, 74.2, 71.7, 72.2, 69.5, 71.9, 71.8, 71.1, 70.9, 73.5, 70.6, 68.9, 71.5, 74.0, 75.8, 75.8, 70.0, 70.2, 64.3, 67.0, 67.6, 70.0, 67.8, 69.2, 71.7, 71.5, 70.6, 72.5, 73.0, 70.4, 68.2, 71.3, 74.9, 74.0, 70.3, 66.5, 72.0, 74.5, 76.6, 71.7, 69.4, 72.5, 71.9, 72.1, 70.9, 72.2)
var.test(June, July, alternative = "two.sided")
June <- c(68.2, 71.4, 67.0, 68.9, 63.4, 66.3, 62.7, 65.9, 69.0, 65.4, 62.5, 68.2, 68.5, 69.8, 63.6, 63.6, 66.5, 66.8, 69.9, 67.5, 67.2, 67.1, 68.8, 67.8, 70.3, 67.1)
July <- c(67.6, 70.0, 67.8, 69.2, 71.7, 71.5, 70.6, 72.5, 73.0, 70.4, 68.2, 71.3, 74.9, 74.0, 70.3, 66.5, 72.0, 74.5, 76.6, 71.7, 69.4, 72.5, 71.9, 72.1, 70.9, 72.2)
CG <- data.frame(cbind(June, July))
SG <- stack(CG)
AR <- aov(values ~ ind, data = SG)
summary(AR)

(a) The probability is 0.1116.

(b) The probability is 0.0000.