| Exam Board | OCR |
|---|---|
| Module | FS1 AS (Further Statistics 1 AS) |
| Year | 2017 |
| Session | Specimen |
| Marks | 10 |
| Topic | Linear regression |
| Type | Hypothesis test for zero correlation |
| Difficulty | Standard +0.3 This is a straightforward application of standard FS1 correlation and regression techniques: calculating a regression line from summary statistics (routine formula application), understanding correlation coefficient properties (standard conceptual knowledge), and performing a hypothesis test using critical values from tables. The final part tests understanding of correlation vs causation, a key concept but requiring only basic reasoning. All parts are textbook-standard with no novel problem-solving required. |
| Spec | 5.08a Pearson correlation: calculate pmcc5.08d Hypothesis test: Pearson correlation5.09c Calculate regression line |
| \(x\) | 9.3 | 9.7 | 9.7 | 9.7 | 9.9 | 10.2 | 10.5 | 11.0 | 10.6 | 10.6 |
| \(y\) | 480 | 501 | 540 | 552 | 547 | 622 | 655 | 701 | 712 | 708 |
The following table gives the mean per capita consumption of mozzarella cheese per annum, $x$ pounds, and the number of civil engineering doctorates awarded, $y$, in the United States in each of 10 years.
\begin{center}
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|}
\hline
$x$ & 9.3 & 9.7 & 9.7 & 9.7 & 9.9 & 10.2 & 10.5 & 11.0 & 10.6 & 10.6 \\
\hline
$y$ & 480 & 501 & 540 & 552 & 547 & 622 & 655 & 701 & 712 & 708 \\
\hline
\end{tabular}
\end{center}
source: www.tylervigen.com
\begin{enumerate}[label=(\roman*)]
\item Find the equation of the regression line of $y$ on $x$. [2]
\end{enumerate}
You are given that the product moment correlation coefficient is 0.959.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{1}
\item Explain whether this value would be different if $x$ is measured in kilograms instead of pounds. [1]
\end{enumerate}
It is desired to carry out a hypothesis test to investigate whether there is correlation between these two variables.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{2}
\item Assume that the data is a random sample of all years.
\begin{enumerate}[label=(\alph*)]
\item Carry out the test at the 10\% significance level. [6]
\item Explain whether your conclusion suggests that manufacturers of mozzarella cheese could increase consumption by sponsoring doctoral candidates in civil engineering. [1]
\end{enumerate}
\end{enumerate}
\hfill \mbox{\textit{OCR FS1 AS 2017 Q8 [10]}}