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Level 3Mathematics and Statistics(Statistics)
91584 (3.12): Evaluate statistically based reports
Credits: Four
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OVERALL LEVEL OF PERFORMANCE
Mathematics and Statistics 91584 (3.12)
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You are advised to spend 60 minutes answering the questions in this booklet.
question one
Kiwi mums secretly access kids' Facebook
Half of New Zealand mothers have accessed their children's Facebook page without their consent, according to an international report.
The AVG Digital Coming of Age study surveyed 4 400 parents of 14 to 17-year-old children in 11 countries, including New Zealand, between January 15 and February 1 of 2012.
The study found 44 per cent of Kiwi respondents had accessed their child's Facebook profile without their consent. Spanish parents were the least trusting, with 61 per cent of parents accessing their teen's Facebook, while at the other end of the spectrum only 9 per cent of Japanese respondents admitted to accessing their teen's profile without consent.
More than half (60 per cent) of Kiwi respondents are “friends” with their children on the social media website.
Source: The New Zealand Herald, April 18, 2012 (abridged)
Additional information:AVG is a company that distributes a range of antivirus and internet security products. AVG commissioned Research Now, a research agency, to conduct this global survey to investigate how technology has changed childhood.
Two of the questions asked in the survey were:
- Do you suspect your teen of accessing illegal music downloads?
- How well a job do you think your child’s school is doing in helping them responsibly navigate the internet?
Assume that 400 parents were randomly selected to be surveyed from each of the 11 countries, and that 200 of the parents from each of these countries were mothers and 200 were fathers.
(a)The report states that “half of New Zealand mothers have accessed their children’s Facebook page without their consent”. However, the survey percentage is not provided.
(i)Supposethe survey percentage was 53%.Construct a confidence interval for the true population percentage and determine whether the confidence interval can be used to support a claim that most (over half) of New Zealand mothers have accessed their children’s Facebook page without their consent.
(ii)Determine the lowest survey percentage that would allow the author of this report to claim that most New Zealand mothers have accessed their children’s Facebook page without their consent.
(b)The article states that “More than half (60 per cent) of Kiwi respondents are ‘friends’ with their children on the social media website.”
The table below shows the survey percentages of the respondents from all the countries with respect to whether they are ‘friends’ with their children on Facebook. (These values were originally presented in the report.)
USA / Canada / Italy / Spain / New Zealand / Australia / UK / Germany / Czech Republic / France / Japan72% / 66% / 66% / 64% / 60% / 57% / 51% / 51% / 50% / 32% / 10%
(i)Identify which country or countries in the table above should not be compared with other countries using the ‘rule of thumb’1/√n and explain why.
(ii)Respondents would need to be a Facebook user themselves in order to be friends with their children on Facebook. Discuss how this could explain some of the differences in these countries’ survey percentages.
(c)One component to consider when evaluating statistically-based reports is the funding for the research. Explain if the funding for the research is a potential issue with this study.
Mathematics and Statistics 91584 (3.12)
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question two
Cat owners more likely to be single
If you're having no luck walking up the aisle, then maybe you should try a stroll through the dog park instead. People with dogs are more lucky in love than those with cats, a new study has shown.And, it seems, Cantabrians will be facing a cold and lonely winter – as 63.3 per cent of the respondents identified themselves as “cat people”.
The Purina New Zealand survey showed that, nationwide, 80.5 per cent of dog owners were either married or in a relationship, while only 60.2 per cent of cat owners were taken.Just over 30 per cent of cat owners were single, compared to 14.6 per cent of dog owners.
About 61 per cent of cat owners said they preferred keeping to themselves, while only 53 per cent of dog owners said the same was true of them.Kennel Club director secretary Richard Brown said that while some people might see cats as a substitute for a significant other, dogs were not viewed in quite the same way by their owners.
The survey was conducted by an independent party in March, with 400 New Zealand respondents.
Source: The Press, May 8, 2012 (abridged)
Additional information: Purina New Zealand is a manufacturer of dog and cat food.The survey was conducted with only cat and dog owners. For every five cat owners in New Zealand there are around three dog owners.
(a)Identify the target population for this survey. Describe some of the key characteristics that the sample of 400 respondents should have so that this sample can be used to make inferences about this target population.
(b)One component to consider when evaluating a statistically-based report is the exact questions asked. Identify a potential difficulty with asking a question which uses the phrase ‘keeping to yourself’.
(c)Could the claim that a higher percentage of cat owners prefer to keep to themselves than dog owners be supported by evidence presented in the report? Construct a confidence interval and interpret this interval as part of your answer. You can assume that within the sample of 400, for every five cat owners there are around three dog owners.
(d)Identify and discuss two potential non-sampling errors, biases, or issues that could be problems in this survey.
Mathematics and Statistics 91584 (3.12)
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question three
Obesity linked to less sleep in childhood
Less sleep in childhood equals more obesity in adulthood. That is the conclusion Otago University researchers have come to – showing a possible link between the obesity epidemic and a suggested decline in the number of hours children are sleeping.
The Dunedin Multidisciplinary Health and Development Study used data collected from 1000 Dunedin people born between 1972 and 1973.The researchers used the "body mass index" of the group at 32 years old when 53 per cent were overweight including 18 per cent who were obese. They set those data against "time in bed" data from group members when they were 5, 7, 9, and 11 years old.
After discounting lifestyle factors, the study showed that "short sleep time in childhood was associated with an increased adult body mass index". "Our findings suggest that sleep restriction could be a plausible contributing factor to the current epidemic of obesity," the study said.
The paper acknowledged that the correlation between lack of sleep in childhood and obesity in adulthood was "weak". "In view of the increasing prevalence of obesity, an effect of this size may have important public health implications."Researcher Dr Erik Landhuis said it was well known children needed an "adequate" amount of sleep.
Source: Otago Daily Times, November 4, 2008 (abridged)
(a)Identify the explanatory and response variables for the study. Discuss any potential issues with the measurement of the explanatory variable.
(b)Explain whether this study is an observational studyor an experiment. Give an implication of using this type of study for the relationship investigated.
(c)The report begins with the statement “less sleep in childhood equals more obesity in adulthood”. Comment on the quality of this statement.
(d)The report states that after discounting lifestyle factors, the study showed that "short sleep time in childhood was associated with an increased adult body mass index".
Give examples of two related lifestyle factors that may need to be taken into account for this study, and explain how these may be confounding variables.
Extra space if required.Clearly number the question (if required).
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Mathematics and Statistics 91584 (3.12)
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Extra space if required.Clearly number the question (if required).
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Mathematics and Statistics 91584 (3.12)