A company says 25% of its customers use its app. After a campaign, a random sample of 30 customers finds that 13 use the app. The company tests, at the 5% level, whether the proportion has increased.
(a)
Write down suitable hypotheses for the test, defining the parameter you use.
(1 mark)
(b)
Carry out the test, stating your conclusion in context.
A spinner is designed so that it lands on red with probability 0.3. Jo suspects the probability is not 0.3. She spins it 40 times and tests at the 5% level.
(a)
Find the critical region for the test. The probability in each tail should be as close as possible to, but not more than, 2.5%.
(4 marks)
(b)
The spinner lands on red 19 times. Comment on Jo's suspicion.
A courier firm says 10% of its deliveries are late. A customer group suspects the proportion is higher. In a random sample of 50 deliveries, 9 are late. The group tests at the 5% level.
(a)
Find the p-value for the test.
(2 marks)
(b)
The firm's manager says: 'The test proves that only 10% of our deliveries are late.' Comment on this statement.
(2 marks)
(c)
Explain, in context, what the 5% significance level means.
The volume of drink in a can is Normally distributed with standard deviation 4 ml. The label says the mean volume is 330 ml. A trading standards officer measures a random sample of 20 cans and finds a mean of 328.6 ml.
Test, at the 5% level, whether the mean volume is less than 330 ml.
Long-term records suggest that the daily mean temperature at Hurn from May to October is Normally distributed with mean 14.8 °C and standard deviation 2.6 °C. A student takes 15 consecutive days from July 2015 in the large data set and finds a mean of 15.9 °C. She tests at the 1% level whether the 2015 mean is higher.
(a)
Find the p-value for her test.
(2 marks)
(b)
State the conclusion of the test in context.
(1 mark)
(c)
Criticise the student's sampling, and explain the effect on her conclusion.
For 15 randomly chosen towns, the product moment correlation coefficient between population density and average commute time is r=−0.505. Critical values for n=15 (one tail): 5%: 0.4409; 2.5%: 0.5140; 1%: 0.5923.
Test, at the 5% level, whether there is correlation between population density and commute time.
What hypothesis tests are on Edexcel A-level Maths?
Year 1: one- and two-tailed tests for the proportion p of a binomial distribution. Year 2: tests for the mean of a Normal distribution with known variance, and tests for zero correlation using the product moment correlation coefficient.
What is a critical region?
The set of values of the test statistic that would lead you to reject H₀. For a binomial test, find it from cumulative probabilities so that its probability is as close as possible to the significance level without going over.
How should I write the conclusion?
Say whether the result is significant, then say what that means in context, with the word 'evidence': for example, 'There is sufficient evidence that the proportion of late deliveries has increased.'
