M140: Introducing Statistics Analysis of the Mustard Seedlings - Statistics Assignment Help

Assignment Task:

Task:

Question 1 (Unit 10) – 24 marks
This question concerns the analysis of the mustard seedlings experiment that you were asked to carry out in Unit 10. You will need to use Minitab to answer parts (b) and (e).
(a) In one or two sentences, describe how your experiment went; for example, mention any diculties that you faced along the way. Then present a table of your results, similar in layout to Table 3 of Unit 10 (Subsection 3.4). Indicate clearly the units in which you made your measurements (for example, millimetres) and the measurements that correspond to seedlings whose stems were cut during their growth. Then proceed to part (b) of the question.

If, however, you were unable to collect data of your own, then state this and explain why. Instead of presenting results in a table, draw stemplots for each of the two samples of data given in Table 1, including only measurements from seedlings whose stems were cut during growth. Also, give the main reason for producing such stemplots in the context of a t-test, and comment on the shape of the stemplots relative to this reason.

Table 1 Lengths of roots (in mm) obtained in a mustard seedlings experiment
Seedlings grown in light Seedlings grown in dark
24 30 21 29 18 27 ? 18 ? ?
42 ? 22 17 27 24 ? 29 31 31
? 32 ? 28 24 26 32 27 40 23
22 25 ? 32 ? 29 35 25 ? 41
In Table 1, measurements given in bold were obtained from seedlings whose stems were cut during their growth. A cross indicates a seed which did not germinate. [6]
To answer the remainder of this question, you should use your own data if you have them. Otherwise, use the data from Table 1.

(b) Run Minitab and type your data into columns headed Light, for lengths of roots of seedlings grown in light, and Dark, for lengths of roots of seedlings grown in the dark, for all the seedlings whose stems you cut. In your answer, provide a list of the data as it appears in your Minitab worksheet. (You should also save a copy of your worksheet in order to be able to work on it again at another time.) Use Minitab to calculate the values of the sample variances of the two columns of data. Include a copy of the relevant Minitab output in your answer.

(c) Using the information you obtained in part (b), check whether it is reasonable to assume that the two samples come from populations whose distributions have a common variance. [3]
(d) To investigate whether light a↵ects root growth (when stems have been cut during growth), a t-test is to be performed on the measurements that you made. Defining and using appropriate notation, state the null and alternative hypotheses of this test. [2]
(e) Use Minitab to perform the appropriate t-test on your data. (You should assume that the assumption of a common population variance is reasonable, regardless of the outcome of your investigation in part (c).) Include a copy of the relevant Minitab output in your answer. What is the result of the t-test? Carefully report your conclusions concerning the question of whether light a↵ects root growth of mustard seedlings. [6]

(f) A reservation about your conclusions in part (e), given the way in which the experiment was designed and carried out, might be that cutting the stems could have di↵erent e↵ects in the light and in the dark. Give two other valid reservations. [4]

Question 2 (Unit 10) – 9 marks
You should not use Minitab to answer this question, but do the calculations ‘by hand’ (using a calculator), showing your working.
A manufacturer claims that a model of mobile phone has a battery life of 1020 minutes (i.e. 17 hours). In order to test this claim, 20 mobile phones of that model were fully charged and then used to perform a range of tasks. One task involved browsing the web continuously until the phones shut down.

The length of time for each phone to shut down was recorded in minutes.
The results are summarised in Table 2.
Table 2 Summary statistics for the battery life
(in minutes) of a model of mobile phone
Task Sample size Mean Standard deviation Web browsing 20 986 49
(a) What is the most appropriate version of the t-test if you want to test the null hypothesis that the underlying population mean battery life for this model of phone is what the manufacturer claims it to be when the phone is used in this way? Justify your choice. [2]
(b) What are the number of degrees of freedom and the 5% critical value for the most appropriate t-test applied to these data? [2]
(c) Hence calculate a 95% confidence interval for the population mean battery life for this model of mobile phone, as measured during this task. [3]
(d) Based on your calculated 95% confidence interval, is it plausible that the underlying population mean battery life is 1020 minutes as claimed by the manufacturer? Justify your answer. [2]

Question 3 (Unit 11) – 5 marks
Rheumatoid arthritis is a common, chronic condition that causes symptoms such as joint pain and restricted movement of the joints. Drugs do not cure rheumatoid arthritis, but they may reduce the symptoms. A medical research team wishes to compare the e cacy of two treatments (drug X and drug Y) that are currently available. It is known that these two treatments will alleviate symptoms only whilst the drug is being taken.
Consider the two designs below in turn. Explain how each of the two designs could be implemented in this context and state which you would recommend, justifying your choice. Your answer should discuss any pros and cons for each type of trial.
• A group-comparative design
• A crossover design [5]

Question 4 (Unit 11) – 6 marks
Several surveys of graduate employers have been conducted to investigate the question ‘what skills do graduate employers look for?’. These core skills are seen as ‘transferable skills’ or ‘employability skills’ and graduates are expected to provide examples demonstrating their competencies in these areas when applying to graduate schemes. Ten skills were identified with the five key core skills given in Table 3.
Table 3 Five core skills that graduate employers look for
A Ability to apply subject knowledge and concepts
B Good communication skills (oral and written)
C Time management and organisation
D Information gathering; interpretation and evaluation
E Adaptability

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