During practice sessions, a basketball coach makes his players run several 'line drills'.
He records the times taken, in seconds, by one of his players to run the first 'line drill' on a random sample of 8 practice sessions. The results are shown below.
\(\begin{array} { l l l l l l l l } 29.4 & 31.1 & 28.9 & 30.0 & 29.9 & 30.4 & 29.7 & 30.2 \end{array}\)
Assuming that these data come from a normal distribution with mean \(\mu\) and variance \(0 \cdot 6\), calculate a \(95 \%\) confidence interval for \(\mu\).
State the two ways in which the method used to calculate the confidence interval in part (a) would change if the variance were unknown.
During a practice session, a player recorded a mean time of 35.6 seconds for 'line drills'.
Give a reason why this player may not be the same as the player in part (a).
Give a reason why this player could be the same as the player in part (a).
In country \(A\), the median daily caffeine intake per student who drinks coffee is 120 mg . A university professor who oversees a foreign exchange programme believes that students visiting from country B drink more coffee and therefore have a greater daily caffeine intake from coffee.
On a randomly chosen day, the caffeine intake, in mg , from coffee consumption by each of 15 randomly selected students from country B is given below.
136
149
202
0
110
0
100
180
0
187
0
0
138
197
115
The professor suspects that the students with zero caffeine intake do not drink coffee, and decides to ignore those students and instead focus on the coffee-drinking students.
Conduct an appropriate Wilcoxon test at a significance level as close to \(5 \%\) as possible. State your conclusion in context.