EXM.1.SL.TZ0.9

pestleMathematicsAISLPaper 1EXM· sl-4-8-binomial-distributionsource ↗

Six coins are tossed simultaneously 320 times, with the following results.

At the 5% level of significance, test the hypothesis that all the coins are fair.

Markscheme / solution

Let H₀ be the hypothesis that all coins are fair, (C1)

and let H₁ be the hypothesis that not all coins are fair. (C1)

Let $T$ be the number of tails obtained, $T$ is binomially distributed. (M1)

(A3)

Notes: Award (A2) if one entry on the third row is incorrect. Award (A1) if two entries on the third row are incorrect. Award (A0) if three or more entries on the third row are incorrect.

$\chi _{{\text{calc}}}^2 = \frac{{{{\left( {5 - 5} \right)}^2}}}{5} + \frac{{{{\left( {40 - 30} \right)}^2}}}{{30}} + \frac{{{{\left( {86 - 75} \right)}^2}}}{{75}} + \frac{{{{\left( {89 - 100} \right)}^2}}}{{100}} + \frac{{{{\left( {67 - 75} \right)}^2}}}{{75}} + \frac{{{{\left( {29 - 30} \right)}^2}}}{{30}} + \frac{{{{\left( {4 - 5} \right)}^2}}}{5}$

$= 7.24$ (A1)

Also $\chi _{0.05{\text{,}}\,\,6}^2 = 12.592$ (A1)

Since 7.24 < 12.592, H₀ cannot be rejected. (R1)

[9 marks]

Examiners’ report

[N/A]