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Date May 2012 Marks available 3 Reference code 12M.3sp.hl.TZ0.1
Level HL only Paper Paper 3 Statistics and probability Time zone TZ0
Command term Determine 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.

[3]
a.

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.

[7]
b.

Markscheme

unbiased estimate of the mean: 795 (grams)     A1

unbiased estimate of the variance: 108 \((gram{s^2})\)     (M1)A1

[3 marks]

a.

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]

b.

Examiners report

A successful question for many candidates. A few candidates did not read the question and adopted a 2-tailed test.

a.

A successful question for many candidates. A few candidates did not read the question and adopted a 2-tailed test.

b.

Syllabus sections

Topic 7 - Option: Statistics and probability » 7.3 » Unbiased estimators and estimates.

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