Lampshells" are special shellfish animals that have fossil records going back 600 million years. Little information is available about present day populations of lampshells. While generally rare they are abundant around parts of New Zealand; especially a particular species called "mermaid toenails". They are seen in shallow water or washed up on beaches. Using scuba diving equipment the researchers selected a random quadrat (2m x 2m) from a surveyed beach and scooped up all the sediment in that quadrat to a depth of 30cm. On shore, the live and dead shells were sorted. They measured the length of every "mermaid toenail" in each group: live and dead. The data is presented in the file "Mermaid shells.xlsx" available on the Moodle page/Assignments. There appeared to be a difference in length, maybe due to longevity of the shells such that the dead shells may be expected to be older on average and so longer.
- Does this design use paired data or independent samples? Explain.
- Calculate the relevant summary statistics from the data?
- Are the conditions satisfactory for a test of significance to be applied? Show your graphical evidence.
- Conduct a test of significance on the difference in means between the live and dead shells to test the hypothesis that the mean length is longer for dead shells. Use a significance level of 0.05.Follow all steps clearly and write a clear conclusion.
- Calculate the mean difference in lengths of the live and dead shells with 90% confidence.