A study was conductedat Down-Under universitybyDr Tatauranga's research team to better understandthe level of physical exercise and body-mass index in university students. The goal was to predict the reduction in BMI that could be expected from implementing aprogramencouraging students to add a 15-minute walk to their daily activities.

A random sample of 28 university students have been asked to wear a physical activity tracker for a week and for each participant, the average number of steps per day (in thousands) was recorded as well as the BMI. The students have been asked to livetheir livesas usual during that week.

The raw data gathered from this study, ready to be copied and pasted in R, is given below.

PAvalues <- c(6, 8.8, 6.1, 6.2, 5.6, 13, 6.2, 9, 8.1, 7.8, 12.2, 7.9, 14, 6, 10, 4.4, 12.5, 11.9, 7.02, 4, 3.8, 10.8, 6.8, 10.5, 10.8, 9.7, 8.5, 5.3)

BMIvalues<- c(32, 30, 25, 27, 27.5, 24, 23, 22, 20, 26, 28, 19, 21, 26, 21, 27, 19, 24.5, 22, 35, 27, 19, 22, 26, 15, 28, 31, 21)

PAvaluesis the number of steps per day for each participant (in thousands).

BMIvaluesis the BMI of each participant (in kilograms per square metre), with participants ordered in the same way as previously.For example, the first participant in the study had a PA value of6(which meansthefirst participant on average took6000 steps per day during that week) and a BMI of32kilograms per square metre.

1 Based on that sample, what BMI would you predict for a student who takes9000steps per day (that is, theirPA = 9)

2 Construct a 85% confidence interval for the true expected change in BMI given an increase in PA by 1 (in other words,an increase in the level of physical activity by 1000 steps per day).

3 Construct a 85% confidence interval for the expected change in BMIwhen students add 1.8 PA to their level of physical activity.