A2 October 2020 Q2

EdexcelCurrent spec6 marksConfidence Intervals

2. Jemima makes jam to sell in a local shop. The jam is sold in jars and the weight of jam in a jar is normally distributed.

Jemima takes a random sample of 8 of her jars of jam and weighs the contents of each jar, \(x\) grams. Her results are summarised as follows

\[\sum x = 3552 \qquad \sum x^2 = 1\,577\,314\]

(a) Calculate a 95% confidence interval for the mean weight of jam in a jar. (5)

The labels on the jars state that the average contents weigh 440 grams.

(b) State, giving a reason, whether or not Jemima should be concerned about the labels on her jars of jam. (1)

Mark scheme (a)

Scheme	Marks	AO
\(\bar{x} = 444\)	M1	2.1
\(s_x^{\,2} = \dfrac{1\,577\,314 - 8 \times 444^2}{7} = \dfrac{226}{7} = 32.2857\ldots\)	A1	1.1b
\(t_7(5\%)\) 2-tail cv = 2.365	B1	1.1b
95% CI for \(\mu\) is: \(444 \pm 2.365 \times \sqrt{\dfrac{32.2857\ldots}{8}}\)	M1	2.1
\(= (439.248\ldots,\ 448.75\ldots)\) = awrt (439, 449)	A1	1.1b
	(5)

1^st M1 for finding mean and attempting \(s^2\)

1^st A1 for correct mean and \(s^2\) (accept awrt 3sf)

B1 for a correct cv of 2.365 or better

2^nd M1 for use of correct formula, ft their mean, \(s_x\) and cv for \(t\) (use of 1.96 is M0)

2^nd A1 for awrt (439, 449)