Penguin Statistics Inference Review

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📊 Part 1: Multiple Choice Questions

1. A researcher collected flipper length data from 50 Gentoo penguins (median = 217mm, IQR = 8mm) and 50 Chinstrap penguins (median = 196mm, IQR = 12mm). Which statement is most accurate?

Gentoo penguins have more variable flipper lengths

Chinstrap penguins have more variable flipper lengths

Both species have equal variability

Cannot determine variability from this information

2. If a dataset is right-skewed, which relationship between measures of centre is typically observed?

Mean = Median

Mean < Median

Mean > Median

No consistent relationship

3. A 95% confidence interval for the difference in mean body mass between Gentoo and Chinstrap penguins is (800g, 1200g). What can we conclude?

There is no significant difference between species

Gentoo penguins are significantly heavier

Chinstrap penguins are significantly heavier

The sample size was too small

4. Which factors affect the width of a confidence interval? (Select all that apply)

Sample size

Confidence level

Population variability

Sample mean

✏️ Part 2: Short Answer Questions

5. The bill length data for Chinstrap penguins shows Q1 = 46.2mm, Q3 = 51.1mm, and contains a measurement of 58.5mm. Determine if 58.5mm is an outlier using the IQR method. Show your working.

6. Explain why we use the median instead of the mean when comparing penguin body mass data that contains outliers.

7. A researcher takes 10 different samples of 30 Gentoo penguins each and calculates the mean flipper length for each sample. Explain why these 10 sample means will not all be identical, even though they're from the same population.

8. The 90% confidence interval for mean Chinstrap penguin bill depth is (18.1mm, 18.9mm). If we increased the sample size but kept the confidence level the same, how would this affect the interval? Explain your reasoning.

🔍 Part 3: Data Interpretation

9. Complete the following interpretation: "We are 95% confident that the true difference in mean body mass between Gentoo and Chinstrap penguins is between _________ and _________. This means that if we repeated this study many times, approximately _____% of our confidence intervals would contain the true population difference."

10. A box plot shows that Gentoo penguin flipper lengths have a longer upper whisker than lower whisker. What does this suggest about the distribution shape? How might this affect your choice of summary statistics?