| Date | May 2012 | Marks available | 7 | Reference code | 12M.3sp.hl.TZ0.1 |
| Level | HL only | Paper | Paper 3 Statistics and probability | Time zone | TZ0 |
| Command term | Test | Question number | 1 | Adapted from | N/A |
Question
A baker produces loaves of bread that he claims weigh on average 800 g each. Many customers believe the average weight of his loaves is less than this. A food inspector visits the bakery and weighs a random sample of 10 loaves, with the following results, in grams:
783, 802, 804, 785, 810, 805, 789, 781, 800, 791.
Assume that these results are taken from a normal distribution.
Determine unbiased estimates for the mean and variance of the distribution.
In spite of these results the baker insists that his claim is correct.
Stating appropriate hypotheses, test the baker’s claim at the 10 % level of significance.
Markscheme
unbiased estimate of the mean: 795 (grams) A1
unbiased estimate of the variance: 108 \((gram{s^2})\) (M1)A1
[3 marks]
null hypothesis \({H_0}:\mu = 800\) A1
alternative hypothesis \({H_1}:\mu < 800\) A1
using 1-tailed t-test (M1)
EITHER
p = 0.0812... A3
OR
with 9 degrees of freedom (A1)
\({t_{calc}} = \frac{{\sqrt {10} (795 - 800)}}{{\sqrt {108} }} = - 1.521\) A1
\({t_{crit}} = - 1.383\) A1
Note: Accept 2sf intermediate results.
THEN
so the baker’s claim is rejected R1
Note: Accept “reject \({H_0}\) ” provided \({H_0}\) has been correctly stated.
Note: FT for the final R1.
[7 marks]
Examiners report
A successful question for many candidates. A few candidates did not read the question and adopted a 2-tailed test.
A successful question for many candidates. A few candidates did not read the question and adopted a 2-tailed test.
