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Slide 1  2.9 Statistical Inference
 All you need to know…mostly!

Slide 2  NZ Herald – 28 April

Slide 3  NZ Herald – 29 April

Slide 4  Overview
 Pose an appropriate comparative investigative question that can be answered using the data provided.
 Collect two samples (of at least 30 each)
 State the method you used to select samples and collect data
 Calculate appropriate statistics from your sample.
 Draw appropriate graphs that show different features of the data in relation to your investigative question.
 Discuss your findings (the hard part!!)
 Make an inference (conclusion) that answers your . question.

Slide 5  Overview
 Pose
 Collect two samples (of 50 each)
 State the method
 Calculate appropriate statistics
 Draw appropriate graphs
 Discuss
 Make an inference

Slide 6  1. POSE THE QUESTION
 Pose a comparative question to be investigated. Comparative means that you are comparing two separate groups. These might be male vs female, adults vs children, rugby stars vs tiddlywink players…
 Your question must identify the two populations very specifically. It’s not “girls and boys” but “the year 12 girls from the census NZ sample and the year 12 boys from the same sample”.
 A prediction regarding the results is made (easy merit!). “I think that my results will show that girls tend to weigh more than boys…”
 Remember: Very Good People CanDo Maths

Slide 7  2. Take your sample
 An appropriate random sample of at least 30 from each group has been generated and the data collected. You should briefly state how you did it.
 Contextual reasons have been given for deciding on the use of a simple random sample or the sample size.
 I will use simple random sampling from Censusatschool 2011 to collect my samples from both the A group and the B group separately from the survey data. I will use a sample of size 30 for each group as this should give me enough information about [the variable] in each group to ensure that the samples for each group are unbiased and representative of the whole population.

Slide 8  3. Calculate your stats
 Include good stats for both your sample groups.
 You must include at least a box and whisker graph. A dot plot overlay is a REALLY good idea because it will give you points to discuss, literally!
 For merit you need informal confidence intervals calculated and plotted – and….
 Don’t forget units!
 informal confidence intervals will be discussed. Rather than a point estimate we should use an interval estimate.

Slide 9  Discuss sample distribution
 Discuss your sample distributions by comparing them. Aim to make at least three different statements describing such things as:
 Box  Middle 50%
 Overlap.
 Interesting or unusual features.
 Summary statistics must be used to help your descriptions.
 Make sure your comments link to your question and the population.
 Comments must be smart and to the point.
 Constantly ‘hammer’ the difference between the sample and population.
 Spread.
 Shift.
 Shape.
 BOSSSI !!!
 Note the icon – click to listen!

Slide 10  Discuss sampling variability
 This is a phrase that means that different samples will produce different statistics (and therefore different conclusions about your population).
 I would expect that if I took more random samples I would get different statistics and that the informal confidence intervals would be slightly different to this sample. The median of the population is likely to be between my informal confidence intervals of S and Q.
 Note the icon – click to listen!

Slide 11  Effect of sample size
 You should talk about the effect of sample size or taking another sample, or the presence of outliers.
 Make all comments in context, and relate them to the informal confidence interval
 Talk about whether the population median would be contained in your sample median.
 I took a sample size of 200. While 30 is the minimum ss for meaningful stats, I wanted a bigger sample because...the effect of outliers would be minimised, it’s easy as C@S does it all, sometimes the subgroups aren’t even (more girls in all my samples)
 I would expect that if I took more random samples I would get different statistics and that the informal confidence intervals would be slightly different to this sample. The median of the population is likely to be between my informal confidence intervals of S and Q.
 Note the icon – click to listen!

Slide 12  7. Answer the question!
 Make a supported correct inference that is stated, in context, for both sets of data in terms of the confidence interval.
 Communicate your findings clearly, and link findings to the context and populations.
 You must show an understanding of the difference between your sample statistics and the conclusions you are making for the population. You are making a very good, educated guess, but the population median will NOT be exactly the same as your sample median!
 Context is KING! Talking clearly about your sample stats and separating them from your population conclusions is VITAL.

Slide 13  7. Answer the question!
 My sample statistics are only estimates for the entire population. I am confident that back in the population the true median height [context] for Group A and Group B will lie within my informal confidence interval, , i.e. between 3.56 and 7.82 [units].
 So from my data I can make the claim that the heights for Year 12 girls in Birkenhead College are significantly smaller than the Year 12 boys as the informal confidence intervals do not overlap.
 Now answer the question! Therefore the student council should be advised to make separate coats for the boys and the girls
 Note the icon – click to listen!