Question 4 - A-Level Maths

OCR MEI S2 2011 June — Question 4

Exam Board	OCR MEI
Module	S2 (Statistics 2)
Year	2011
Session	June
Topic	Chi-squared distribution

In a survey on internet usage, a random sample of 200 people is selected. The people are asked how much they have spent on internet shopping during the last three months. The results, classified by amount spent and sex, are shown in the table.

\multirow{2}{*}{}		Sex		\multirow{2}{*}{Row totals}
		Male	Female
\multirow{5}{*}{Amount spent}	Nothing	28	34	62
	Less than £50	17	21	38
	£50 up to £200	22	26	48
	£200 up to £1000	23	16	39
	£1000 or more	8	5	13
Column totals		98	102	200

Write down null and alternative hypotheses for a test to examine whether there is any association between amount spent and sex of person. The contributions to the test statistic for the usual \(\chi ^ { 2 }\) test are shown in the table below.
\multirow{2}{*}{} Sex
Male Female
\multirow{5}{*}{Amount spent} Nothing 0.1865 0.1791
Less than £50 0.1409 0.1354
£50 up to £200 0.0982 0.0944
£200 up to £1000 0.7918 0.7608
£1000 or more 0.4171 0.4007
The sum of these contributions, correct to 3 decimal places, is 3.205.
Calculate the expected frequency for females spending nothing. Verify the corresponding contribution, 0.1791 , to the test statistic.
Carry out the test at the \(5 \%\) level of significance, stating your conclusion clearly.

A bakery sells loaves specified as having a mean weight of 400 grams. It is known that the weights of these loaves are Normally distributed and that the standard deviation is 5.7 grams. An inspector suspects that the true mean weight may be less than 400 grams. In order to test this, the inspector takes a random sample of 6 loaves. Carry out a suitable test at the \(5 \%\) level, given that the weights, in grams, of the 6 loaves are as follows.
\(\begin{array} { l l l l l l } 392.1 & 405.8 & 401.3 & 387.4 & 391.8 & 400.6 \end{array}\) RECOGNISING ACHIEVEMENT

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