UserWiki:Gryfall

SGTA
In November 2018, levels of PM2.5 recorded at the Earlwood monitoring site in Sydney had a mean of 7.92 μg/m3. A random sample of 300 measurements of PM2.5 levels at this same site in November 2019 had a mean of 14.04 μg/m3 and a standard deviation of 16.56 μg/m3.

Were mean PM2.5 levels recorded at the Earlwood monitoring site in November 2019 significantly different to those recorded in November 2018?

What is interval within which it can be ascertained, with 95% confidence, that a value in subsequent tests would fall?

$$CI=\hat{y}\pm t_{crit}\times\frac{s}{\sqrt{n}}\longrightarrow 14.04\pm 1.967930\times\frac{16.56}{\sqrt{300}}$$ $$=14.04\pm 1.88152221963$$ $$\approx 12.16, 15.92$$

95% of any repeated test values will fall between 12.16 and 15.92μg/m3.

Prac
The pulse after running on the spot has a larger range and higher values overall, including the mean and median.

This is a paired set of data because the measured variable, pulse, is linked to the same person. The pulse is measured once before exercise and once afterward.

The distribution of the differences between pulses 1 and 2 has a range of around 50bpm, with most of the differences between 10 and 20bpm.

$$CI=\hat{y}_d\pm confidence\ level\longrightarrow 17.741935483871\pm 5.44713120962281$$ $$=12.29480427, 23.18906669$$

SGTA 2
A representative sample of 320 university students was surveyed to determine which of the following attributes would have the greatest influence on their choice of a laptop computer for their studies: price, portability, speed or technical support. The gender of each student was also recorded. A laptop distributor claims that 50% of university students consider price to be the most important consideration when buying a laptop for study, 20% consider technical support is the most important consideration with the other students evenly divided between those who consider portability to be the most important factor and those who consider speed the most important factor.

Are student considerations when buying a laptop for study as claimed by the distributor?