Question 4. [16 marks]

Historical temperature records from Newcastle Nobbys Signal Station suggest that the

average maximum temperature in summer (i.e., December, January and February) from

1960-2009 was 21.75 degrees Celsius. To investigate whether this has changed since 2009,

a random sample of 44 summer maximum temperatures from Newcastle Nobbys Signal

Station was taken from 2010-2022. The maximum temperature data are in the vector

maxtemp stored in the file SummerMaxTemp.txt.

The mean and standard deviation of the maximum temperature data are 7 = 24.768

degrees Celsius and 8 = 3.659 degrees Celsius, as shown in the following R code:

summertemp = read. table ("SummerMaxTemp.txt", header = TRUE)

mean (summertemp$Maxtemp)

## [1] 24.76818

ad (summertemp$Maxtemp)

3

## [1] 3.659316

qt (0.975, 43)

## [1] 2.016692

(a) [4 marks] Using the formula from the course notes, compute a 95% confidence

interval for the population mean maximum temperature in summer at Newcastle

Nobbys Signal Station from 2010-2022. While you may use a function in R to verify

your answer, it is expected that you show the steps of working out the limits of the

confidence interval via hand working. You may use R to perform the calculations

required for these steps.

(b) [2 marks] Based on the confidence interval derived in part (a), is there any evidence

that the average maximum temperature in summer from Newcastle Nobbys Signal

Station from 2010-2022 is higher than the average maximum temperature over the

period 1960-2009?