Introduction to statistics

Question

The Department of Meteorological Services (DMS) in Gaborone has been issuing warning about expected increases in temperatures in the coming days. A researcher wanted to know how some students at UB could have been affected by the heat stress already. Out of a population of 1750 students the researcher selected a sample of 160 students. Assuming a proportion of 15%, what is the approximate probability that more than 10% of the sample would report that they have already experienced extreme levels of heat?

Answer 1

A very short solution:

p = 0.15, n = 160

SE = sqrt((0.15 × 0.85)/160) = 0.028

z = (0.10 - 0.15)/0.028 = -1.77

P(p̂ > 0.10) = P(z > -1.77) ≈ 0.96

1. Answer: 0.96