Note: For all questions in this assignment that require you to use a two-sample t-test, always use the non-pooled procedure (that is, the procedure that assumes population standard deviations are not equal).

Note: if your t-table does not include the correct df value, please round down to the next available df value.

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1. A study compared floral diversity between croplands and wetlands. Independent random samples of 120 cropland regions and 61 wetland regions were obtained in the Southern Great Plains. The cropland regions contained an average of 15.03 native floral species, with a standard deviation of 4.83; the wetland regions had an average of 16.76 and a standard deviation of 4.95.

(a) Test if the mean number of native floral species is lower in cropland regions. Use the 1% significance level. (8 marks)

(b) Obtain a two-sided 99% confidence interval for the difference in mean number of floral species between cropland and wetland regions. (4 marks)

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3. According to an online source, 79.8% of students are right-handed in Alberta secondary schools, 7.9% are left-handed, and 12.3% are ambidextrous (source: Census at School Canada, 2018-2019). A researcher wishes to test if these percentages seem reasonable among the general population of Albertans, so she obtains a random sample of 200 Albertans, from which she obtains the following frequency distribution: