Page 1 of 24 M.Sc. in Plant Genetics and Crop Improvement, XXXXXXXXXX Module BIO-7038Y: Plant Breeding & Statistics Statistics Assignment 001 Uninvigilated examination. This question paper is...

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Page 1 of 24 M.Sc. in Plant Genetics and Crop Improvement, 2019-19 Module BIO-7038Y: Plant Breeding & Statistics Statistics Assignment 001 Uninvigilated examination. This question paper is available from 15h00 on Thursday 6th February 2020. Answers must be submitted as a hard copy (using this answer template) to the HUB by 15h00 on Thursday 13th February 2020. Answers must be your own unaided work. You may use course notes, textbooks and other written sources. Collaboration or collusion with other students taking this exam is not permitted under any circumstances. It is also not permitted under any circumstances for you to ask for or receive advice on the exam from any other person. The paper contains 10 questions for a total of 160 marks. Answer all questions. Candidates are advised to write clearly because no credit can be given for illegible answers. All answers must be written within the boxes. The questions in this exam use data in the file ‘BIO-7038Y_2019-20_stats_exam_1.xlsx’ which is available on the Blackboard site. Congratulations on your appointment as an oat breeder at Highland Plants Ltd, the leading plant breeding company in the far north of Scotland. Please answer the following questions. 1. You have measured the percent lipid content of 25 samples each of two oat varieties. The data are in the worksheet 'Q1'. a) Give the mean and median percent lipid content of Gordon oats. (2 marks) Mean Median Page 2 of 24 b) Use a boxplot to display the averages and distributions of percent lipid content of the two varieties, Gordon and Hector. If you paste a printed graph into the box, make sure it’s stuck down firmly. (3 marks) c) Explain why the boxplot may cause you to suspect the accuracy of one of the data points. (2 marks) Page 3 of 24 d) On checking the original scoresheet, you see there was a typing mistake and that the correct value was 10.33%. Correct this point in the spreadsheet, draw the boxplot again (you are not required to show the revised boxplot here) and state two conclusions you can make from this graph about differences between the varieties Gordon and Hector. You do not need to do any calculations to answer this question. (3 marks) • • e) Give the mean and median percent lipid content of Gordon oats in the revised dataset. (2 marks) Mean Median f) Explain why one of these statistics changes compared to Q1(a) when the mistaken value is corrected but the other does not. (3 marks) 15 marks in total for Question 1. Page 4 of 24 2. The current market leading variety is Duncan and you wish to compare it to a new variety, Macbeth. In oats, shorter straw is desirable. Use worksheet ‘Q2’, which contains data from a preliminary trial in which the lengths of 20 stems of each variety have been measured. a) You wish to test if Macbeth has shorter straw than Duncan. State appropriate null and alternative hypotheses to be tested. (2 marks) b) Give the standard deviation and the standard error of the mean straw length of these two oat varieties. (3 marks) c) You need to conduct a t-test to test the hypotheses you stated in Q2(a). First, explain briefly whether you should do a one-sided or two-sided test. (2 marks) Page 5 of 24 d) Now comment on the difference between the variances (or standard deviations) of the samples of the two varieties. Explain briefly whether you should do a t-test in which the variance is pooled across the varieties, or one in which a separate variance is used for each variety. (3 marks) e) Conduct an appropriate two-sample t-test to test the hypotheses you stated in Q2(a). State your conclusions. (4 marks) Page 6 of 24 f) Give the lower 95% confidence limit for the difference of the mean straw lengths of Duncan and Macbeth. Does this support your conclusion in Q2(e)? (2 marks) 16 marks in total for Question 2. 3. Continuing your comparison of Duncan and Macbeth, you wish to test if the two varieties differ in grain yield. This is a complex trait which is often affected by on-farm conditions. Use the data in worksheet ‘Q3’ on yield (tonnes per hectare) in trials at 15 sites. a) State null and alternative hypotheses about the difference in yield of these two varieties. (2 marks) b) Explain why you should do a paired-sample t-test to compare the yields of Duncan and Macbeth in this dataset. (2 marks) Page 7 of 24 c) Conduct a paired-sample t-test to test the hypotheses you stated in Q3(a). State the main assumptions you have made in conducting this test. Show a summary of your working. State your conclusions regarding the hypothesis test. (8 marks) d) Calculate a 95% confidence interval for the difference in yield of Duncan and Macbeth. Does your answer support your conclusion in Q3(c)? (5 marks) Page 8 of 24 e) In a t-test which ignores the potential influence of trial site on yield, the P-value is 0.10 and the 95% confidence interval for the difference in the yields of Duncan and Macbeth is (−1.28, 0.13) t/ha. Explain why the conclusion of this test differs from that which you found in Q3(c) and Q3(d). You may find it helpful to view a graph of the yields of the two varieties plotted against one another but you are not expected to present a graph here. (4 marks) 21 marks in total for Question 3. 4. Another important trait in oats is the percent kernel content, the amount of the grain which consists of the edible kernel or groat. Higher kernel content is desirable. You wish to test if three oat varieties differ in their mean percent kernel content. Data on 10 batches of grain of each variety are in worksheet ‘Q4’. a) State null and alternative hypotheses about the kernel content of the three varieties. (2 marks) Page 9 of 24 b) Draw a dot histogram to inspect the variation between the varieties. If you paste a graph into this box, make sure it is stuck down firmly. (2 marks) c) State your main conclusions from the dot histogram. (3 marks) Page 10 of 24 d) Conduct a one-way analysis of variance to test the hypothesis you stated in Q4(a) and present the anova table. What conclusion can you make from the anova table? (4 marks) e) Test the significance of the pairwise differences between all three pairs of varieties, using a Bonferroni adjustment. Show your working. (4 marks) 15 marks in total for Question 4. Page 11 of 24 5. You wish to know about the relationship of specific weight, the mass per unit volume of grain, to percent kernel content. You have measured on the mean value of both traits from a panel of 30 breeding lines of oats. Specific weight is measured in kg per hectolitre (100 litres of grain). Data are in worksheet ‘Q5’. a) State null and alternative hypotheses about the relationship of kernel content to specific weight. (2 marks) b) Draw a graph to display the relationship of specific weight (the dependent variable) to kernel content in these oat varieties. If you paste a graph into this box, make sure it is stuck down firmly. (3 marks) Page 12 of 24 c) What does this graph tell you about the relationship of specific weight to kernel content? (2 marks) d) Give the Pearson correlation coefficient between kernel content and specific weight. (2 marks) e) Do a linear regression of specific weight against percent kernel content. Here, present the anova table and state what conclusion you can make from this table. (4 marks) f) What proportion of variation in specific weight is explained by variation in kernel content in this dataset? (2 marks) Page 13 of 24 g) From the results of the linear regression, write down the equation which relates specific weight to kernel content. (2 marks) h) By how much would you expect specific weight to increase for a 0.1% increase in percent kernel content? Show your working. (2 marks) 19 marks in total for Question 5. 6. Experiments and field trials are often designed in blocks such that each the experimental units within a block are exposed to similar conditions