Please read the Assessment Guide on the module website before beginning work on this TMA. You can submit your TMA either by post or electronically using the University’s online TMA/EMA service.
This TMA is marked out of 100. Your overall score for this TMA will be the sum of your marks for each question.
The marks allocated to each part of each question are indicated in brackets in the margin.
Guidance about how to answer TMA questions is given in Subsection 7.2 of Unit 1.
Note that the Minitab files that you require for this assignment should be downloaded from the ‘Assessment’ area on the module website.
Please note that you should round you answers to an appropriate level of accuracy.
If you have a disability that makes it difficult for you to attempt any of these questions, then please contact your Student Support Team or your tutor for advice.
You should be able to answer Questions 1 and 2 after you have studied Unit 6.
You should be able to answer Questions 3 and 4 after you have studied Unit 7. You will need to use Minitab to answer Question 4.
You should be able to answer Questions 5 and 6 after you have studied Unit 8. You will need to use Minitab to answer Question 6.
You should be able to answer Questions 7 and 8 after you have studied Unit 9. You will need to use Minitab to answer Questions 7 and 8.
(a) A researcher is interested in studying childhood obesity in the UK. She downloads some data from the government website relating to overweight children. This data was collected through the National Child Measurement Programme (NCMP) and a child is defined as obese based on their BMI measurement. The latest data that she finds is for the period 2017 to 2018; this data is split by ethnicity and given for children aged 4 to 5 years old and 10 to 11 years old. The number of children in these age ranges that are not considered to be obese is also given.
The data is summarised and shown in Table 1.
In this question we will consider the case where one child is selected at random.
(i) Complete Table 1 by calculating the missing entries, and the column, row and overall totals. Present these as part of a table. [3]
(ii) Calculate the probability that the selected child is obese and is 4 to 5 years old. [2]
(iii) Calculate the probability that the selected child is black, obese and is 10 to 11 years old. [2]
(iv) Calculate the probability that a 4 to 5 year old obese child is not white. Show all of your working. [3]
(b) Emily, Rebecca and Caroline are training for a marathon. They need to train by running several times a week over a six-week period. The probability that on a particular day Emily chooses to run is 0.45, for Rebecca this probability is 0.25, and for Caroline this probability is 0.3.
What is the probability that all three will choose to run on the same day?
State any important assumption that you make in order to calculate this probability. [3]
A scientist wants to investigate the effects of climate change in the UK. The rainfall in 12 regions of the United Kingdom is recorded for February 2008 and 2018. Table 2 gives the total rainfall, in mm, along with the differences between the rainfall in February 2008 and 2018. This data comes from the Met Office and is shown in Table 2.
A sign test is to be performed to investigate whether the rainfall recorded in February 2018 differs from the rainfall recorded in February 2008.
(a) Write down the hypothesis to be tested. [2]
(b) Record the number of values lying above and the number lying below the hypothesised value. What is the value of the test statistic? [2]
(c) What is the appropriate critical value at the 5% significance level? [1]
(d) Decide whether or not you would reject the hypothesis at the 5% significance level. [1]
(e) Using Figure 6 of Unit 6 (Subsection 4.1), calculate the p-value given by the hypothesis test. [3]
(f) Looking at this p-value, and using Table 10 of Unit 6 (Subsection 5.1), what conclusion can be drawn from the hypothesis test? [1]
(g) How does this conclusion sit with the result of part (d)? [1]
(h) What is your overall conclusion in terms of the difference in rainfall in February 2008 and February 2018, based on these data? [1]
(a) For the normal distribution shown in Figure 1, find approximate values for its mean and standard deviation. Explain how you obtained your answers. [3]
(b) (i) The normal distribution of a variable x has mean µ = 70 and standard deviation σ = 5. Sketch this distribution. [3]
(ii) Write down the formula for z that converts each value of the variable x in part (b)(i) so that z follows a standard normal distribution. Your answer should contain both the general formula and the specific formula for this example. [2]
(iii) Calculate the value of z corresponding to x = 61. [1]
(iv) Interpret the value of z in terms of the number of standard deviations x is above or below its mean. [2]
(c) Suppose that the population distribution of weights of bags of cement produced in a factory has mean 10 kg and standard deviation 0.05 kg.
(i) Find the standard deviation of the sampling distribution of the mean weight for samples of 50 bags of cement. [2]
(ii) Hence give the approximate distribution of the mean weight for samples of 50 such bags of cement. [2]
You will need to use Minitab to answer this question.
A random sample of mobile phone prices from one store in 2019 were collected. The sample size, mean and standard deviation are presented in Table 3.
Table 3
Sample size Mean price (£) Standard deviation (£) 44 531.10 337.90
The overall population mean mobile phone price was £548.80.
A one-sample z-test is to be performed to investigate whether the mean mobile phone price in the store was the same as the population mobile phone price in all stores in 2019.
(a) Using appropriate notation, which you should define, specify the null and alternative hypotheses associated with the test. [2]
(b) Use Minitab to perform a one-sample z-test on the mobile phone price data. Include a copy of the relevant Minitab output in your answer. What is the value of the test statistic? [3]
(c) Give the p-value from the test performed in part (b), and say what may be concluded from the test in terms of evidence about the hypotheses. Relate your conclusions back to consideration of the mean mobile phone price from this store. [3]
(d) Suppose that in addition, a sample of size greater than 25 of phone prices was also obtained from a different store in 2019. The researchers proposed to use a two-sample z-test to make an appropriate comparison regarding the two stores. Using appropriate notation, which you should define, specify the null and alternative hypotheses that would be associated with this test. [2]
Yuliya is training for a triathlon. She is confident with her cycling, so is concentrating on running and swimming while training. It turns out that:
• on 55% of the days she goes running
• of the days that she goes running, on 60% of these days she also goes swimming.
(a) Let R denote the event Yuliya goes running while training, and let S denote the event that Yuliya goes swimming.
Write the information given in the two bullet points in symbolic form. [2]
(b) Calculate the probability that on a randomly chosen day Yuliya chooses to go running and swimming while training. [3]
(c) Additional information is now given that Yuliya goes swimming on 50% of the days. Calculate the probability that on a randomly chosen day, while training, when Yuliya has chosen to go swimming that she also goes running. [3]
(d) What is the probability that Yuliya chooses to run or swim, or both while training? [2]
(e) For Yuliya, while training, are the events of running and swimming independent? Give a reason for your answer. [2]
You will need to use Minitab to answer this question.
The Minitab file that you require for this question should be downloaded from the ‘Assessment’ area on the module website.
Table 4 shows NHS data relating to children and young people with eating disorders. Recorded are the waiting times before treatment is started for routine cases in a number of regions in England. The data covers the period 2018–19.
CS 340 Milestone One Guidelines and Rubric Overview: For this assignment, you will implement the fundamental operations of create, read, update,
Retail Transaction Programming Project Project Requirements: Develop a program to emulate a purchase transaction at a retail store. This
7COM1028 Secure Systems Programming Referral Coursework: Secure
Create a GUI program that:Accepts the following from a user:Item NameItem QuantityItem PriceAllows the user to create a file to store the sales receip
CS 340 Final Project Guidelines and Rubric Overview The final project will encompass developing a web service using a software stack and impleme
