3.State whether the following statements are true or false, and provide a brief
i. For a set of observations x1, x2,...,xn,
set of observations x1, x2,...,xn, with mean ¯x, then:
(xi x¯) > 0.
ii. For two independent events A and B such that P(A) > 0 and P(B) > 0,
P(A [ B) < P(A) + P(B).
iii. For a random variable X, E(X2) can be less than (E(X))2.
iv. Rejecting a true null hypothesis is known as the power of a test.
v. A 4-by-2 contingency table which results in a 2 test statistic value of
6.724 is statistically significant at the 5% significance level.
5.(a) A 20.0 L container at 303 K holds a mixture of two gases with a total pressure of 5.00
here are 2.00 mol of Gas A in the mixture, how many moles of Gas B are present? (R = 0.0821 L • atm/(K • mol))
(b) The gas in a 250. mL piston experiences a change in pressure from 1.00 atm to 2.80 atm. What is the new volume (in mL) assuming the moles of gas and temperature are held constant?
(c) Small quantities of Oxygen can be produced by the decomposition of mercury(II) oxide as shown below. Typically, the oxygen gas is bubbled through water for collection and becomes saturated with water vapor. Atomic weight of HgO = 216.6 amu, Atomic weight of Oxygen = 32.00 amu)
2 HgO(s) → 2 Hg(ℓ) + O₂(g)
(i) Assuming that 3.05 grams of HgO was used in this reaction, determine the number of moles of oxygen gas formed.(According to the above chemical equation)
(ii) Assuming 310. 0 mL of Oxygen gas was collected at at 29°C, calculate the pressure of the Oxygen gas that was collected. (R = 0.0821 L • atm/(K • mol)
(iii) If the vapor pressure of water at this temperature equals to 0.042 atm, calculate the pressure reading of this experiment.
7.Let a = sin b, 0 < b < pi/2.
Find, in terms of b, the solutions of sin 2x =
So far I just tried to do the obvious and substitute -a for - sin b. Like so;
sin 2x = - sin b
which then becomes;
sin 2x = sin -b
and then I can remove the sines and rearrange for x, which gives me this.
2x = -b
x = -b/2
However, if I were to look at the domain of b. Any value within the domain will give a value that doesn't fit the domain of x. Any suggestions would be great. Thank you!
You are asked to carry out a study on behalf of a business analytics specialised consultancy on a subsample
on a subsample of weekly data from Randall’s Supermarket, one of the biggest in the UK. Randall’s marketing management team wishes to identify trends and patterns in a sample of weekly data collected for a number of their loyalty cardholders during a 26-week period. The data includes information on the customers’ gender, age, shopping frequency per week and shopping basket price. Randall’s operates two different types of stores (convenient stores and superstores) but they also sell to customers via an online shopping platform. The collected data are from all three different types of stores. Finally, the data provides information on the consistency of the customer’s shopping basket regarding the type of products purchased. These can vary from value products, to brand as well as the supermarket’s own high-quality product series Randall’s Top. As a business analyst you are required to analyse those data, make any necessary modifications in order to determine whether for any single customer it is possible to predict the value of their shopping basket.
Randall’s marketing management team is only interested in identifying whether the spending of the potential customer will fall in one of three possible groups including:
• Low spender (shopping basket value of £25 or less)
• Medium Spender (shopping basket value between £25.01 and £70) and
• High spenders (shopping basket greater than £70)
For the purpose of your analysis you are provided with the data set Randall’s.xls. You have to decide, which method is appropriate to apply for the problem under consideration and undertake the necessary analysis. Once you have completed this analysis, write a report for the Randall’s marketing management team summarising your findings but also describing all necessary steps undertaken in the analysis. The manager is a competent business analyst himself/herself so the report can include technical terms, although you should not exceed five pages. Screenshots and supporting materials can be included in the appendix.
After completing your analysis, you should submit a report that consists of two parts. Part A being a non-technical summary of your findings and Part B a detailed report of the analysis undertaken with more details.
Part A: A short report for the Head of Randall’s Marketing Management (20 per cent). This should briefly explain the aim of the project, a clear summary and justification of the methods considered as well as an overview of the results.
Although, the Head of Randall’s Marketing Management team who will receive this summary is a competent business analytics practitioner, the majority of the other team members have little knowledge of statistical modelling and want to know nothing about the technical and statistical underpinning of the techniques used in this analysis. This report should be no more than two sides of A4 including graphs, tables, etc. In this report you should include all the objectives of this analysis, summary of data and results as well as your recommendations (if any).
Part B: A technical report on the various stages of the analysis (80 per cent).
The analysis should be carried out using the range of analytics tools discussed:
• SPSS Statistics
Ensure that the exercise references:
• Binary and multinomial logistic regression
• Linear vs Logistic regression
• Logit Model with odds Ratio
• Co-efficients and Chi Squared
• MLR co-efficients
• Assessing usefulness of MLR model
• Interpreting a model
• Assessing over-all model fit with Psuedo R-Squared measures
• Classification accuracy (Hit Ratio)
• Wald Statistic
• Odd ratio exp(B)
• Ratio of the probability of an event happening vs not happening
• Ratio of the odds after a unit change in the predictor to the original odds
• Residuals analysis
• Cook’s distance
• Adequacy (with variance inflation factor VIF and tolerance statistic)
• Outliers and influential points cannot just be removed. We need to check them (typo? – unusual data?)
• Check for multicollinearity
Write a short and concise report to explain the technical detail of what you have done for each step of the analysis.
The report should also cover the following information:
• Any type of analysis that might be useful and check whether the main assumptions behind the analyses do not hold or cannot be
• Give evidence of the understanding of the statistical tools that you are using. For example, comment on the model selection procedure and the coefficient interpretation, e.g. comment on the interpretation of the logistic regression coefficients if such a method is used and provide an example of
• Conclusions and explanation, in non-technical terms, of the main points