1.1. A charity running four sloth sanctuaries across a wild area of South America records data on all the sloths in its care. The numbers of sloths at the four sanctuaries are 24, 40, 16 and 56. To compare care across the 4 sanctuaries the charity decides to take a sample of sloths from each sanctuary and run some health tests on the sloths selected.

For the sanctuary with 40 sloths in its care, identify the sampling frame and briefly describe how the charity could efficiently use a three-digit random number generator to select the sloths from this sanctuary.

1.2. The charity decides to use a sampling fraction of one-eighth from each sanctuary. Determine the total number of sloths that will be selected for the health tests.

1.3. The results from the health tests showed that the sloths at the sanctuary with the smallest population weighed, on average, less than those from the other three sanctuaries, whereas the average weights of the sloths in those other three sanctuaries were similar.

Suggest a reason why this does not necessarily mean that the sloths at the sanctuary with the smallest population are in poorer health than those at the other three sanctuaries.

1.4. The charity wishes to determine which sloths are suitable for release into the wild. A sloth can be released once it has reached the age of 3 and is of a healthy weight. Explain why the information from the sample conducted by the charity is of little use to them in determining which sloths are suitable for release into the wild.