| Exam Board | SPS |
|---|---|
| Module | SPS SM Statistics (SPS SM Statistics) |
| Year | 2022 |
| Session | February |
| Marks | 12 |
| Topic | Type I/II errors and power of test |
| Type | Carry out hypothesis test |
| Difficulty | Easy -1.3 This is a straightforward statistics question testing basic concepts: advantages of sampling, stratified sampling benefits, outlier identification using IQR, and a standard one-sample z-test. All parts are routine recall or textbook procedures with no novel problem-solving required. The hypothesis test is particularly standard with the population SD conveniently given. |
| Spec | 2.01a Population and sample: terminology2.01c Sampling techniques: simple random, opportunity, etc2.02g Calculate mean and standard deviation2.05e Hypothesis test for normal mean: known variance |
| Mean |
| Median |
|
| ||||||
| 21.0 | 4.20 | 20.5 | 18.0 | 22.9 |
14. Zac is planning to write a report on the music preferences of the students at his college. There is a large number of students at the college.
\begin{enumerate}[label=(\alph*)]
\item State one reason why Zac might wish to obtain information from a sample of students, rather than from all the students.
\item Amaya suggests that Zac should use a sample that is stratified by school year.
Give one advantage of this method as compared with random sampling, in this context.
Zac decides to take a random sample of 60 students from his college. He asks each student how many hours per week, on average, they spend listening to music during term. From his results he calculates the following statistics.
\begin{center}
\begin{tabular}{ | c | c | c | c | c | }
\hline
Mean & \begin{tabular}{ c }
Standard \\
deviation \\
\end{tabular} & Median & \begin{tabular}{ c }
Lower \\
quartile \\
\end{tabular} & \begin{tabular}{ c }
Upper \\
quartile \\
\end{tabular} \\
\hline
21.0 & 4.20 & 20.5 & 18.0 & 22.9 \\
\hline
\end{tabular}
\end{center}
\item Sundip tells Zac that, during term, she spends on average 30 hours per week listening to music.
Discuss briefly whether this value should be considered an outlier.
\item Layla claims that, during term, each student spends on average 20 hours per week listening to music. Zac believes that the true figure is higher than 20 hours. He uses his results to carry out a hypothesis test at the $5 \%$ significance level.
Assume that the time spent listening to music is normally distributed with standard deviation 4.20 hours.
Carry out the test.\\[0pt]
\\[0pt]
\\[0pt]
\\[0pt]
\\[0pt]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM Statistics 2022 Q14 [12]}}