9231/41/M/J/25q1

The manager of a hardware store is interested in whether there is a difference in the amount spent per customer on weekdays ($x) compared to weekends ($y). Random samples of 120 customers on weekdays and 80 customers on weekends are taken and the amount spent by each customer is recorded. The results are summarised as follows:

, , ,

Test at the 1% significance level whether there is a difference in the mean amount spent per customer on weekdays compared to weekends. You should not assume that the population variances of the amounts spent on weekdays and weekends are equal. [7 marks]

Mark Scheme

9231/41/M/J/25q4

A researcher is interested in whether there is a difference between two schools in students’ aptitude for English. She randomly chooses 10 students from school X and 8 students of a similar age from school Y to take a written English test. The scores for the students from school X (x) and school Y (y) are summarised as follows: , , , . You should assume that the two distributions are normal and have the same population variance.

(a) Find a 95% confidence interval for the difference in the mean scores for students from school X and students from school Y in the written English test. [6 marks]

(b) Use the confidence interval you found in part (a) to explain why there is insufficient evidence at a 5% significance level to suggest that the English scores of students from school X and students from school Y are different. [1 mark]

Mark Scheme

9231/43/M/J/25q2

A farmer is investigating whether using a new fertiliser will increase the yield of tomato plants. The farmer selects 40 tomato plants at random and gives them the new fertiliser. The crop mass, x kg, of each of these 40 plants is recorded. The farmer selects a further 60 tomato plants at random and gives them a standard fertiliser. The crop mass, y kg, of each of these 60 plants is recorded. The results are summarised as follows:

, , ,

Find a 90% confidence interval for the difference in mean crop mass associated with each type of fertiliser. [7 marks]

9231/43/M/J/25q5

A doctor is investigating the concentration of blood glucose in patients at risk of developing type 2 diabetes, where blood glucose is measured in appropriate units. The doctor claims that a particular intervention reduces the concentration by more than k units on average. A group of 8 at risk patients is selected at random and each patient follows the intervention for six months. The blood glucose concentrations before and after the intervention are given in the following table.

Patient	A	B	C	D	E	F	G	H
Before	183	165	172	165	143	176	161	153
After	164	148	164	149	134	153	155	148

(a) Use a t-test at the 5% significance level to find the range of values of k for which the result of the test is to reject the null hypothesis. [7 marks]

(b) State an assumption necessary for the test in part (a) to be valid. [1 mark]

Mark Scheme