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Inferential Statistics · Paper 2 — Free Maths AA SL Practice Questions

1MasterySAQ-SZ-scores and t-tests6 marksPaper 2~9 min
A biologist measures the wingspan, in mm, of a sample of 1212 butterflies from a certain species. The results are as follows: 48.2, 51.7, 49.5, 52.3, 50.1, 47.8, 50.9, 49.3, 51.6, 48.9, 51.4, 50.848.2,\ 51.7,\ 49.5,\ 52.3,\ 50.1,\ 47.8,\ 50.9,\ 49.3,\ 51.6,\ 48.9,\ 51.4,\ 50.8 The biologist claims that the mean wingspan of this species is 50.0 mm50.0\,\text{mm}.
(a)
Calculate the sample mean and the sample standard deviation of the wingspans. [2 marks]
(b)
Calculate the value of the tt-test statistic for a one-sample tt-test of the biologist's claim. [2 marks]
(c)
The test is conducted at the 5%5\% significance level. State the critical value and determine whethere is sufficient evidence to reject the biologist's claim. [2 marks]
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