Edexcel FS2 AS (Further Statistics 2 AS) 2018 June

1. The scores achieved on a maths test, \(m\), and the scores achieved on a physics test, \(p\), by 16 students are summarised below.

$$\sum m = 392 \quad \sum p = 254 \quad \sum p ^ { 2 } = 4748 \quad \mathrm {~S} _ { m m } = 1846 \quad \mathrm {~S} _ { m p } = 1115$$

1. Find the product moment correlation coefficient between \(m\) and \(p\)
2. Find the equation of the linear regression line of \(p\) on \(m\) Figure 1 shows a plot of the residuals. \begin{figure}[h]
   \includegraphics[alt={},max width=\textwidth]{0fcb4d83-9763-4edd-8006-93f75a44c596-02_808_1222_997_429} \captionsetup{labelformat=empty} \caption{Figure 1}
   \end{figure}
3. Calculate the residual sum of squares (RSS). For the person who scored 30 marks on the maths test,
4. find the score on the physics test. The data for the person who scored 20 on the maths test is removed from the data set.
5. Suggest a reason why. The product moment correlation coefficient between \(m\) and \(p\) is now recalculated for the remaining 15 students.
6. Without carrying out any further calculations, suggest how you would expect this recalculated value to compare with your answer to part (a).
   Give a reason for your answer.

   V349 SIHI NI IMIMM ION OC

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1. The continuous random variable X has probability density function

$$f ( x ) = \begin{cases} \frac { 1 } { 8 } & 1 \leqslant x \leqslant 9
0 & \text { otherwise } \end{cases}$$

1. Write down the name given to this distribution. The continuous random variable \(Y = 5 - 2 X\)
2. Find \(\mathrm { P } ( Y > 0 )\)
3. Find \(\mathrm { E } ( Y )\)
4. Find \(\mathrm { P } ( Y < 0 \mid X < 7.5 )\)

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1. The table below shows the heights cleared, in metres, for each of 6 competitors in a high jump competition.

These 6 competitors also took part in a long jump competition and finished in the following order, with C jumping the furthest.
C
A
F
D
B
E

1. Calculate Spearman's rank correlation coefficient for these data.
2. Stating your hypotheses clearly, test at the \(5 \%\) level of significance whether or not there is a positive correlation between results in the high jump and results in the long jump. The product moment correlation coefficient between the height of the high jump and the length of the long jump for each competitor is found to be 0.678
3. Use this value to test, at the \(5 \%\) level of significance, for evidence of positive correlation between results in the high jump and results in the long jump.
4. State the condition required for the test in part (c) to be valid.
5. Explain what your conclusions in part (b) and part (c) suggest about the relationship between results in the high jump and results in the long jump.

   V349 SIHI NI IMIMM ION OC

   VJYV SIHIL NI LIIIM ION OO

   VJYV SIHIL NI JIIYM ION OC

1. The continuous random variable \(X\) has cumulative distribution function

$$\mathrm { F } ( x ) = \left\{ \begin{array} { l r } 0 & x < 3
c - 4.5 x ^ { n } & 3 \leqslant x \leqslant 9
1 & x > 9 \end{array} \right.$$ where \(c\) is a positive constant and \(n\) is an integer.

1. Showing all stages of your working, find the value of \(c\) and the value of \(n\)
2. Find the lower quartile of \(X\)