Question 1
Paper 2Hard14 marksA field ecologist investigates whether bee visits differ between a mown and an unmown meadow. There is one meadow of each type. For the first investigation, 30 distinct bee visits were randomly selected from each meadow and classified by duration.
| Meadow | Less than 10 s | 10 s to less than 20 s | 20 s or more | Total |
|---|---|---|---|---|
| Mown | 8 | 12 | 10 | 30 |
| Unmown | 14 | 10 | 6 | 30 |
| Total | 22 | 22 | 16 | 60 |
For a separate investigation, a random sample of 12 distinct bee visits was taken from each meadow. The sample means and sample standard deviations of visit duration were as follows.
| Meadow | Sample size | Mean duration (s) | Sample standard deviation (s) |
|---|---|---|---|
| Mown | 12 | 21.4 | 4.8 |
| Unmown | 12 | 16.1 | 5.2 |
Assume the two populations of visit durations are normally distributed, have equal variances, and were sampled independently. Use a 5% significance level for each test.
State the null and alternative hypotheses for a chi-squared test of independence between meadow type and visit-duration category. Show that the expected frequencies for the mown meadow are 11, 11 and 8.
Using your GDC, find the degrees of freedom, chi-squared statistic and p-value for the test. State your conclusion.
The ecologist predicts that the population mean visit duration is greater in the mown meadow. State suitable hypotheses and use your GDC to carry out an appropriate test. Give the p-value and a conclusion.
The ecologist concludes that mowing causes longer bee visits and changes the distribution of visit-duration categories. Assess this conclusion in light of the results and the fieldwork design.