Practice Paper 3 (Statistics) (Edexcel A Level Maths: Mechanics)

Medhi is a meteorologist investigating the weather in Heathrow and claims that there is negative correlation between the daily total rainfall, f mm, and daily total sunshine, s hours.

Write down suitable null and alternative hypotheses to test Medhi’s claim.

Medhi decides to use the large data set to investigate this claim and forms a sample using all the days in June 2015 relating to Heathrow. 

Some values for the daily total rainfall are labelled as “tr”. Using your knowledge of the large data set, state the range of values Mehdi could assign to these values.

Medhi calculates the product moment correlation coefficient as r = 0.2659 using all the days in June.

Test, at the 5% level of significance, whether there is negative correlation between daily total rainfall and daily total sunshine.

Medhi uses this data to calculate the equation for the regression line of f on s. He plans to use the regression line to predict the amount of rainfall there will be in Heathrow during a day in December.

Give two reasons why this is unlikely to produce a reliable estimate.

Hugo, a newly appointed HR administrator for a company, has been asked to investigate the number of absences within the IT department.  The department contains 23 employees, and the box plot below summarises the data for the number of days that individual employees were absent during the previous quarter.

An outlier is an observation that falls either more than 1.5  (interquartile range) above the upper quartile or less than 1.5 (interquartile range) below the lower quartile.

Show that these data have an outlier, and state its value.

For the 23 employees within the department, Hugo has the summary statistics:

 = 286  and  ²= 4238

Hugo investigates the employee corresponding to the outlier value found in part (a) and discovers that this employee had a long-term illness.  Hugo decides not to include that value in the data for the department.

Assuming that there are no other outliers, calculate the mean and standard deviation of the number of days absent for the remaining employees.

A discrete random variable  has the probability distribution shown in the following table:

	-1	1	2

Find the value of .

X  is sampled twice such that the results of the two experiments are independent of each other, and the outcomes of the two experiments are recorded.  A new random variable,Y, is defined as the sum of the two outcomes.

Complete the following probability distribution table for Y:

	-2	0	1	2	3	4

Find:

The IQ of a student at Calculus High can be modelled as a random variable with the distribution . The headteacher decides to play classical music during lunchtimes and suspects that this has caused a change in the average IQ of the students.

Write suitable null and alternative hypotheses to test the headteacher’s suspicion.

The headteacher selects 10 students and asks them to complete an IQ test.  Their scores are:

127, 127, 129, 130, 130, 132, 132, 132, 133, 138

Test, at the 5% level of significance, whether there is evidence to support the headteacher’s suspicion.

It was later discovered that the 10 students used in the sample were all in the same advanced classes.

Comment on the validity of the conclusion of the test based on this information.

The following diagram shows the distribution of heights, in cm, of adult men in the UK:

The distribution of heights follows a normal distribution, with a mean of 175.3 cm and a standard deviation of 7.6 cm.

Write down the values of the height that correspond to:

Use the properties of the normal distribution to determine whether each of the following statements is likely to be true. In each case give a reason for your answer.

Paul, a renowned mathematics educationalist, has a height of 196 cm.

Find the percentage of adult men in the UK who have a height that is less than Paul’s.

A supermarket wants to gather data from its shoppers on how far they have travelled to shop there. One lunchtime an employee is stationed at the door of the shop for half an hour and instructed to ask every customer how far they have travelled.