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Summary study book Teaching Classics with Technology of (13) - ISBN: 9781350086272 (Good)
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Statistics and Probability [166marks]
Juliet is a sociologist who wants to investigate if income affects
happiness amongst doctors. This question asks you to review Juliet’s
methods and conclusions.
Juliet obtained a list of email addresses of doctors who work in her city. She
contacted them and asked them to fill in an anonymous questionnaire.
Participants were asked to state their annual income and to respond to a set of
questions. The responses were used to determine a happiness score out of 100. Of
the 415 doctors on the list, 11 replied.
1a. Describe one way in which Juliet could improve the reliability of her [1 mark]
investigation.
Markscheme
Any one from: R1
increase sample size / increase response rate / repeat process
check whether sample is representative
test-retest participants or do a parallel test
use a stratified sample
use a random sample
Note: Do not condone:
Ask different types of doctor
Ask for proof of income
Ask for proof of being a doctor
Remove anonymity
Remove response K .
[1 mark]
1b. Describe one criticism that can be made about the validity of Juliet’s [1 mark]
investigation.
, Markscheme
Any one from: R1
non-random sampling means a subset of population might be responding
self-reported happiness is not the same as happiness
happiness is not a constant / cannot be quantified / is difficult to measure
income might include external sources
Juliet is only sampling doctors in her city
correlation does not imply causation
sample might be biased
Note: Do not condone the following common but vague responses unless they
make a clear link to validity:
Sample size is too small
Result is not generalizable
There may be other variables Juliet is ignoring
Sample might not be representative
[1 mark]
Juliet’s results are summarized in the following table.
1c. Juliet classifies response K as an outlier and removes it from the data. [1 mark]
Suggest one possible justification for her decision to remove it.
, Markscheme
because the income is very different / implausible / clearly contrived R1
Note: Answers must explicitly reference "income" to get credit.
[1 mark]
For the remaining ten responses in the table, Juliet calculates the mean happiness
score to be 52. 5.
1d. Calculate the mean annual income for these remaining responses. [2 marks]
Markscheme
($) 90 200 (M1)A1
[2 marks]
1e. Determine the value of r, Pearson’s product-moment correlation [2 marks]
coefficient, for these remaining responses.
Markscheme
r = 0. 558(0. 557723 …) A2
[2 marks]
Juliet decides to carry out a hypothesis test on the correlation coefficient to
investigate whether increased annual income is associated with greater
happiness.
1f. State why the hypothesis test should be one-tailed. [1 mark]
, Markscheme
EITHER
only looking for change in one direction R1
OR
only looking for greater happiness with greater income R1
OR
only looking for evidence of positive correlation R1
[1 mark]
1g. State the null and alternative hypotheses for this test. [2 marks]
Markscheme
H0 : ρ = 0; H1 : ρ > 0 A1A1
Note: Award A1 for ρ seen (do not accept r), A1 for both correct hypotheses,
using their ρ or r. Accept an equivalent statement in words, however
reference to “correlation for the population” or “association for the population”
must be explicit for the first A1 to be awarded.
Watch out for a null hypothesis in words similar to “Annual income is not
associated with greater happiness”. This is effectively saying ρ ≤ 0 and should
not be condoned.
[2 marks]
1h. The critical value for this test, at the 5% significance level, is 0. 549. [2 marks]
Juliet assumes that the population is bivariate normal.
Determine whether there is significant evidence of a positive correlation between
annual income and happiness. Justify your answer.
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