Practice questions covering hypothesis testing from this specification. Attempt the questions below, then use the past-paper references to find more on Pearson's site.
Questions to attempt
6 questions on Hypothesis testing, each with its mark scheme and worked method. Reveal the answer when you have had a go.
FS1-4.1 · Extend ideas of hypothesis tests to test for the mean of a Poisson distribution.
Q1
ORIGINAL
Year 1
Year 1: this is the AS subject content the exam board publishes, which is what most schools teach in Year 12.
1.
Under H0, defects occur at a mean rate of 2.5 per hour. Eight independent hours give a total of 28 defects. Test at a 5% significance level whether the mean rate has increased. State the critical region and the size of the test.
(7)
(Total for Question 1 is 7 marks)
FS1-4.1 · Extend ideas of hypothesis tests to test for the mean of a Poisson distribution.
Q2
ORIGINAL
Year 1
Year 1: this is the AS subject content the exam board publishes, which is what most schools teach in Year 12.
2.
A manager claims that the mean number of alerts per shift is 4.2. State hypotheses to test whether the mean has increased, defining your parameter.
(2)
(Total for Question 2 is 2 marks)
FS1-4.1 · Extend ideas of hypothesis tests to test for the mean of a Poisson distribution.
Q3
ORIGINAL
Year 1
Year 1: this is the AS subject content the exam board publishes, which is what most schools teach in Year 12.
3.
A Poisson model has mean 1.8 events per batch. Twelve independent batches produce 14 events in total. Carry out a test at the 5% significance level of whether the mean per batch has decreased, giving the critical region, its size and your conclusion.
(8)
(Total for Question 3 is 8 marks)
FS1-4.2 · Extend hypothesis testing to test for the parameter p of a geometric distribution.
Q4
ORIGINAL
Year 2
Year 2: this is content the exam board adds beyond the AS subject content, for the full A-level.
4.
Six independent geometric observations count trials to first success. Test H0:p=0.3 against H1:p>0.3 at the 5% level of significance using their sum S. Find the critical region and its size, then state the conclusion when S=9.
(7)
(Total for Question 4 is 7 marks)
FS1-4.2 · Extend hypothesis testing to test for the parameter p of a geometric distribution.
Q5
ORIGINAL
Year 2
Year 2: this is content the exam board adds beyond the AS subject content, for the full A-level.
5.
A geometric model uses p=0.35. State hypotheses for testing whether the probability of success has fallen, and state which tail of the waiting time is critical.
(3)
(Total for Question 5 is 3 marks)
FS1-4.2 · Extend hypothesis testing to test for the parameter p of a geometric distribution.
Q6
ORIGINAL
Year 2
Year 2: this is content the exam board adds beyond the AS subject content, for the full A-level.
6.
Five independent geometric observations have common parameter p. Use their sum S to test H0:p=0.4 against H1:p<0.4 at the 5% level. Determine the critical region and its size, then carry out the test and state your conclusion when S=19.
(8)
(Total for Question 6 is 8 marks)
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10 past-paper references · 5 open at the question's page · newest series first
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