Questions FS2 (54 questions)

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Edexcel FS2 Specimen Q4
  1. The times, \(x\) seconds, taken by the competitors in the 100 m freestyle events at a school swimming gala are recorded. The following statistics are obtained from the data.
\cline { 2 - 4 } \multicolumn{1}{c|}{}No. of competitorsSample mean \(\overline { \boldsymbol { x } }\)\(\sum \boldsymbol { x } ^ { \mathbf { 2 } }\)
Girls883.155746
Boys788.956130
Following the gala, a mother claims that girls are faster swimmers than boys. Assuming that the times taken by the competitors are two independent random samples from normal distributions,
  1. test, at the \(10 \%\) level of significance, whether or not the variances of the two distributions are the same. State your hypotheses clearly.
  2. Stating your hypotheses clearly, test the mother's claim. Use a \(5 \%\) level of significance.
Edexcel FS2 Specimen Q5
  1. Scaffolding poles come in two sizes, long and short. The length \(L\) of a long pole has the normal distribution \(\mathrm { N } \left( 19.6,0.6 ^ { 2 } \right)\). The length \(S\) of a short pole has the normal distribution N(4.8, 0.32). The random variables \(L\) and \(S\) are independent.
A long pole and a short pole are selected at random.
  1. Find the probability that the length of the long pole is more than 4 times the length of the short pole. Show your working clearly. Four short poles are selected at random and placed end to end in a row. The random variable \(T\) represents the length of the row.
  2. Find the distribution of \(T\).
  3. Find \(\mathrm { P } ( | L - T | < 0.2 )\)
Edexcel FS2 Specimen Q6
  1. A random sample of 10 female pigs was taken. The number of piglets, \(x\), born to each female pig and their average weight at birth, \(m \mathrm {~kg}\), was recorded. The results were as follows:
Number of piglets, \(\boldsymbol { x }\)45678910111213
Average weight at
birth, \(\boldsymbol { m } \mathbf { ~ k g }\)
1.501.201.401.401.231.301.201.151.251.15
(You may use \(\mathrm { S } _ { x x } = 82.5\) and \(\mathrm { S } _ { m m } = 0.12756\) and \(\mathrm { S } _ { x m } = - 2.29\) )
  1. Find the equation of the regression line of \(m\) on \(x\) in the form \(m = a + b x\) as a model for these results.
  2. Show that the residual sum of squares (RSS) is 0.064 to 3 decimal places.
  3. Calculate the residual values.
  4. Write down the outlier.
    1. Comment on the validity of ignoring this outlier.
    2. Ignoring the outlier, produce another model.
    3. Use this model to estimate the average weight at birth if \(x = 15\)
    4. Comment, giving a reason, on the reliability of your estimate.
Edexcel FS2 Specimen Q7
  1. Over a period of time, researchers took 10 blood samples from one patient with a blood disease. For each sample, they measured the levels of serum magnesium, \(s \mathrm { mg } / \mathrm { dl }\), in the blood and the corresponding level of the disease protein, \(d \mathrm { mg } / \mathrm { dl }\). One of the researchers coded the data for each sample using \(x = 10 s\) and \(y = 10 ( d - 9 )\) but spilt ink over his work.
The following summary statistics and unfinished scatter diagram are the only remaining information. $$\sum d ^ { 2 } = 1081.74 \quad \mathrm {~S} _ { d s } = 59.524$$ and $$\sum y = 64 \quad \mathrm {~S} _ { x x } = 2658.9$$ \(d \mathrm { mg } / \mathrm { dl }\)
\includegraphics[max width=\textwidth, alt={}, center]{e777c787-0d39-4d84-a0f9-fc4a6712184f-22_983_1534_840_303}
  1. Use the formula for \(\mathrm { S } _ { x x }\) to show that \(\mathrm { S } _ { s s } = 26.589\)
  2. Find the value of the product moment correlation coefficient between \(s\) and \(d\).
  3. With reference to the unfinished scatter diagram, comment on your result in part (b).