Stats

• When analysing markets, a range of assumptions are made about the rationality of economic agents involved in the transactions
• The Wealth of Nations was written

  1776
• Rational


  (in classical economic theory) economic agents are able to consider the outcome of their choices and recognise the net benefits of each one
• Rational agents will select the choice which presents the highest benefits
• Producers act rationally by


  Selling goods/services in a way that maximises their profits
• Workers act rationally by


  Balancing welfare at work with consideration of both pay and benefits
• Governments act rationally by


  Placing the interests of the people they serve first in order to maximise their welfare
• Rationality in classical economic theory is a flawed assumption as people usually don't act rationally
• Marginal utility


  The additional utility (satisfaction) gained from the consumption of an additional product
• If you add up marginal utility for each unit you get total utility
• Mark Scheme (RESULTS) Pearson Edexcel GCSE (9 – 1) In Statistics (1ST0) Higher Paper 2H
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• Summer 2021 Publications Code 1ST0_2H_MS All the material in this publication is copyright © Pearson Education Ltd 2021
• General marking guidance These notes offer general guidance, but the specific notes for examiners appertaining to individual questions take precedence.
• All candidates must receive the same treatment. Examiners must mark the last candidate in exactly the same way as they mark the first.
• Where some judgement is required, mark schemes will provide the principles by which marks will be awarded; exemplification/indicative content will not be exhaustive. When examiners are in doubt regarding the application of the mark scheme to a candidate's response, the response should be sent to review.
• All the marks on the mark scheme are designed to be awarded; mark schemes should be applied positively. Examiners should also be prepared to award zero marks if the candidate's response is not worthy of credit according to the mark scheme. If there is a wrong answer (or no answer) indicated on the answer line always check the working in the body of the script (and on any diagrams), and award any marks appropriate from the mark scheme.
• Questions where working is not required: In general, the correct answer should be given full marks. Questions that specifically require working: In general, candidates who do not show working on this type of question will get no marks – full details will be given in the mark scheme for each individual question.
• Crossed out work This should be marked unless the candidate has replaced it with an alternative response.
• Choice of method If there is a choice of methods shown, mark the method that leads to the answer given on the answer line. If no answer appears on the answer line then mark both methods as far as they are identical and award these marks.
• Incorrect method If it is clear from the working that the "correct" answer has been obtained from incorrect working, award 0 marks.
• Follow through marks Follow through marks which involve a single stage calculation can be awarded without working as you can check the answer, but if ambiguous do not award. Follow through marks which involve more than one stage of calculation can only be awarded on sight of the relevant working, even if it appears obvious that there is only one way you could get the answer given.
• Ignoring subsequent work It is appropriate to ignore subsequent work when the additional work does not change the answer in a way that is inappropriate for the question or its context. (eg an incorrectly cancelled fraction when the unsimplified fraction would gain full marks). It is not appropriate to ignore subsequent work when the additional work essentially makes the answer incorrect (eg incorrect algebraic simplification).
• Probability Probability answers must be given as a fraction, percentage or decimal. If a candidate gives a decimal equivalent to a probability, this should be written to at least 2 decimal places (unless tenths). Incorrect notation should lose the accuracy marks, but be awarded any implied method marks. If a probability fraction is given then cancelled incorrectly, ignore the incorrectly cancelled answer.
• Range of answers Unless otherwise stated, when an answer is given as a range (eg 3.5 – 4.2) then this is inclusive of the end points (eg 3.5, 4.2) and all numbers within the range.
• Guidance on the use of abbreviations within this mark scheme M method mark awarded for a correct method or partial method A accuracy mark (awarded after a correct method; if no method is seen then full marks for the question are implied but see individual mark schemes for more details) B unconditional accuracy mark (no method needed) oe or equivalent cao correct answer only ft follow through (when appropriate as per mark scheme) sc special case dep dependent (on a previous mark) indep independent awrt answer which rounds to isw ignore subsequent working
• A firm increases advertising

  Demand curve shifts right
• Demand curve shifting right

  Increases the equilibrium price and quantity
• Normal Distribution


  A continuous probability distribution that describes the occurrence of independent events, with a symmetrical bell-shaped curve and no outliers.
• Normal Distribution in Real-Life
• Limits of Normal Distribution

  The normal distribution assumes independence, homoscedasticity, and linearity, but real-world data may exhibit skewness, kurtosis, outliers, or non-normality.
• Outliers in Statistical Analysis

  Outliers can bias results, increase variance, mask patterns, and lead to incorrect inferences. Data transformation, Winsorization, and robust estimation can help mitigate the impact.
• Outliers in Regression


  Outliers can bias coefficients, increase variance, mask relationships, and reduce R-squared. Data transformation, Winsorization, and robust estimation can help mitigate the impact.
• Common Outlier Types


  Freak events, data entry errors, instrumentation errors, human error, anomalies, novelty detection, noise, contamination, and heteroscedasticity are common types of outliers.
• Alicia would like to know if there is a difference in the average price between two brands of shoes. She selected and analyzed a random sample of 40 different types of Brand A shoes and 33 different types of Brand B shoes. Alicia observes that the boxplot of the sample of Brand A shoe prices shows two outliers. Alicia wants to construct a confidence interval to estimate the difference in population means. Is the sampling distribution of the difference in sample means approximately normal?

  Yes, because the size of each sample is at least 30.
• Last year the mean cost for a one-bedroom rental in a certain city was $1,200 per month. Eli is looking for a one-bedroom apartment and is investigating whether the mean cost is less now than what it was last year. A random sample of apartments had a sample mean of $1,180 per month. Assuming all conditions for inference are met, Eli will conduct a hypothesis test as part of his investigation. Which of the following is the correct set of hypotheses?

  Ho: mean=1200

  Ha: mean<1200
• A sociologist will conduct a two-sample -test for a difference in means to investigate whether there is a significant difference, on average, between the salaries of people with bachelor's degrees and people with master's degrees. From a random sample of 32 people with a bachelor's degree, the average salary was $55,000 with standard deviation $3,500. From a random sample of 28 people with a master's degree, the average salary was $58,000 with a standard deviation of $4,000. With a null hypothesis of no difference in the means, which of the following is the test statistic for the appropriate test to investigate whether there is a difference in population means (master's degree minus bachelor's degree) ?

  t=(58000-55000)/square root ((4000)^2/28)+((3500)^2/32
• A reporter responsible for the food section of a magazine investigated the belief that grocery stores sell beef at a higher price in the fall than in the spring. The reporter selected independent random samples of grocerystore beef prices in November and April and computed the mean and standard deviation for the samples. Which of the following are the correct null and alternative hypotheses for the reporter's investigation, where represents the mean price of beef in the fall and represents the mean price of beef in the spring?


  Ho: mean of F- mean of S =0

  Ha: mean of F- mean of S >0
• A sports equipment researcher investigated how different types of wood used to make baseball bats might affect batting. The researcher selected a sample of 80 batters from summer baseball leagues and randomly assigned the batters to one of two groups: the ash bat group or the maple bat group. The mean number of hits for each group was recorded at the end of the season, and the difference in the sample means was calculated. Which of the following is the appropriate inference procedure for analyzing the results of the investigation?

  A two-sample -interval for a difference between population means