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Penguin Statistics Inference Review

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Penguin Statistics Inference Review

Use the study information and data displays to investigate penguin measurements. Show calculations where asked, and explain what the statistics suggest. All measurements are from samples.

Compare the samples

A wildlife team measured 50 penguins of each species. Gentoo flipper lengths had a median of 217 mm and an interquartile range (IQR) of 8 mm. Chinstrap flipper lengths had a median of 196 mm and an IQR of 12 mm.

1.Which sample has the greater spread in its middle half of flipper lengths? Explain how the data show this.

2.Which statement is best supported by the medians?

The typical Gentoo flipper is longer by 21 mm.
The typical Chinstrap flipper is longer by 21 mm.
Every Gentoo flipper is longer than every Chinstrap flipper.
The two species have identical typical flipper lengths.

Investigate unusual values

In a Chinstrap bill-length sample, the lower quartile (Q1) is 46.2 mm and the upper quartile (Q3) is 51.1 mm. A bill length of 58.5 mm is recorded. Use the IQR rule: values above Q3 + 1.5 × IQR or below Q1 − 1.5 × IQR are potential outliers.

3.Work out the IQR and upper outlier fence, then decide whether 58.5 mm is a potential outlier. Show your working.

4.The team finds one unusually heavy penguin in a body-mass sample. Which measure of centre is usually less affected by this extreme value: the mean or the median? Give a reason.

Read the interval

For the difference in mean body mass, Gentoo minus Chinstrap, a study reports a 95% confidence interval of 800 g to 1,200 g.

5.Does this interval provide evidence of a difference in population mean body mass? Which species has the greater estimated mean? Explain using the interval.

6.Complete the interpretation: “We are 95% confident that the true difference in mean body mass (Gentoo minus Chinstrap) is between g and g.”

7.A team keeps the confidence level the same but measures many more penguins. What will usually happen to the width of its confidence interval, and why?

8.Which change would usually make a confidence interval wider, if other factors stay the same?

Use a larger sample.
Choose a higher confidence level.
Reduce the variability in the measurements.
Collect measurements with no variation.

Think about sampling and shape

A researcher takes 10 different random samples of 30 Gentoo penguins from the same population and calculates one mean flipper length for each sample.

9.Why are the 10 sample means unlikely to be exactly identical?

10.A box plot of a penguin measurement has a longer upper whisker than lower whisker. What might this suggest about the distribution, and which pair of measures would be sensible to report if it is strongly skewed?

11.A 90% confidence interval for mean Chinstrap bill depth is 18.1 mm to 18.9 mm. If the sample size increases while the confidence level and population variability stay about the same, predict how the interval is likely to change.