Questions PURE (178 questions)

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OCR PURE Q10
9 marks Easy -1.2
The masses of a random sample of 120 boulders in a certain area were recorded. The results are summarized in the histogram. \includegraphics{figure_5}
  1. Calculate the number of boulders with masses between 60 and 65 kg. [2]
    1. Use midpoints to find estimates of the mean and standard deviation of the masses of the boulders in the sample. [3]
    2. Explain why your answers are only estimates. [1]
  2. Use your answers to part (b)(i) to determine an estimate of the number of outliers, if any, in the distribution. [2]
  3. Give one advantage of using a histogram rather than a pie chart in this context. [1]
OCR PURE Q11
8 marks Moderate -0.3
Casey and Riley attend a large school. They are discussing the music preferences of the students at their school. Casey believes that the favourite band of 75% of the students is Blue Rocking. Riley believes that the true figure is greater than 75%. They plan to carry out a hypothesis test at the 5% significance level, using the hypotheses \(H_0: p = 0.75\) and \(H_1: p > 0.75\). They choose a random sample of 60 students from the school, and note the number, \(X\), who say that their favourite band is Blue Rocking. They find that \(X = 50\).
  1. Assuming the null hypothesis to be true, Riley correctly calculates that \(P(X = 50) = 0.0407\), correct to 3 significant figures. Riley says that, because this value is less than 0.05, the null hypothesis should be rejected. Explain why this statement is incorrect. [1]
  2. Carry out the test. [5]
    1. State which mathematical model is used in the calculation in part (b), including the value(s) of any parameter(s). [1]
    2. The random sample was chosen without replacement. Explain whether this invalidates the model used in part (b). [1]
OCR PURE Q12
4 marks Easy -2.3
This question deals with information about the populations of Local Authorities (LAs) in the North of England, taken from the 2011 census. \includegraphics{figure_6} Fig. 1 and Fig. 2 both show strong correlation, but of two different kinds.
  1. For each diagram, use a single word to describe the kind of correlation shown. [1]
  2. For each diagram, suggest a reason, in context, why the correlation is of the particular kind described in part (a). [2]
Fig. 3 is the same as Fig. 2 but with the point \(A\) marked. Fig. 4 shows information about the same LAs as Fig. 2 and Fig. 3. \includegraphics{figure_7}
  1. Point \(A\) in Fig. 3 and point \(B\) in Fig. 4 represent the same LA. Explain how you can tell that this LA has a large population. [1]