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# Statistics

Question | Answer |
---|---|

Define population | The whole set of items that are of interest |

Define sample | Some subset of the population intended to represent the population |

Define sampling unit | Each individual thing in the population that can be sampled |

Define sampling frame | Often sampling units of a population are individually named or numbered to for a list |

Define census | Data collected from the entire population |

Define simple random sample | -Each sample has an equal chance of selection -Each item has number -Random number generator |

Advantages of simple random sample | -No bias -Easy -Cheap -Equal selection chance |

Disadvantages of simple random sample | -Not suitable for large population -Sampling frame needed |

Define systematic sample | -Elements ordered into list -Every kth element -k=pop size/samp size -Start at random number between 1 and k |

Advantages of systematic sample | -Simple -Quick -Suitable for large populations |

Disadvantages of systematic sample | -Sampling frame needed -Can introduce bias is sampling frame is not random |

Define stratified sample | -Population divided into strata -Simple random sample for each group -Samp size/pop size sampled from each group -Used when sample is large and divided into groups |

Advantages of stratified sample | -Reflects population structure -Proportional representation within population |

Disadvantages of stratified sample | -Population clearly classified into strata -Selection within strata suffer from same disadvantages as simple random |

Define quota sample | -Population divided into groups according to sampling frame -Interviewer selects quotas to reflect groups proportions |

Advantages of quota sample | -Small sample is still representative -Easy -Cheap -Comparable |

Disadvantages of quota sample | -Can introduce bias -Population divided into groups -Non responses not recorded |

Define opportunity sample | Sample taken from people at the time, who meet criteria |

Advantages of opportunity sample | -Easy -Cheap |

Disadvantages of opportunity sample | -Not representative -Dependant on researcher |

What is the equation for a stratified sample | Strata size x sample size/total population |

What is the difference between qualitative and quantitative data | Qualitative- Descriptive Quantitative- Numerical |

What is the difference between discreet and continuous data | Discreet- Only takes certain values Continuous- Takes all values |

How do we find outliers | Greater than Q3+k(Q3-Q1) Less than Q1-k(Q3-Q1) |

Define cleaning the data | Removing outliers |

What do we plot for cumulative frequency diagrams | End point against cumulative frequency |

What is the equation for frequency density | Frequency density=(Frequency x k)/Class width |

When do we use a histogram | Continuous data |

When do we use a bar chart | Discreet data |

What do we comment on when comparing data | -Measure of location -Measure of spread |

What axis is the independent variable on | X |

What axis is the dependent variable on | Y |

Define bivariate | There are pairs of values for two variable |

Define causal relationship | Change in one variables causes a change in the other |

Define interpolation | Estimating a variable within the data range |

Define extrapolation | Estimating a variable outside the data range |

What is the purpose of a regression line | To minimise standard deviation |

When can we use regression lines | For data within the data range |

Define mutually exclusive | If one event happens the other events can't happen |

If events are mutually exclusive: P(A or B)= | P(A)+P(B) |

Define independent events | One event has no effect on the other |

If events are independent P(A and B)= | P(A) x P(B) |

Define random variable | A variable whose value depends on the outcome of a random event |

Define discreet uniform distribution | All probabilities are the same |

ΣP(X=x)= | 1 |

When can you model a random variable with a binomial distribution | -Fixed no of trials(n) -2 possible outcomes -Fixed probability of success (P) -Trials are independent of each other |

P(X<Y)= | P(X≤Y-1) |

P(X≥Y)= | 1-P(X≤Y-1) |

P(X>Y)= | 1-P(X≤Y) |

Define test statistic | The result of the experiment or the statistic that is calculated |

Define null hypothesis | The hypothesis you assume to be correct |

Define alternate hypothesis | Tells you about the parameter if your assumption is wrong |

Define critical region | A region of the probability distribution which if the test statistic falls within it would cause you to reject the null hypothesis |

Define critical value | The first value to fall in the critical region |

What is the actual significance level | The probability of incorrectly rejecting the null hypothesis |

What are the steps of a one tailed hypothesis test | -Formulate a model for test statistic -Identify suitable null and alternate hypotheses -Calculate the probability of test statistic being observed assuming null hypothesis is true -Compare to significance level -Write conclusion in context of question |

What must you do for a two tailed hypothesis test | Halve the significance level |

If y+ax^n then logy= | loga+nlogx |

If y=kb^x then logy= | logk+xlogb |

What does the PMCC describe | The strength and direction of the correlation |

When can the PMCC be used | If there is LINEAR correlation |

If we are hypothesis testing for correlation what are the null and alternate hypothesis | H0: p=0 H1: p≠0 |

How do we write, the probability that B occurs given that A has already occurred | P(P|A) |

What is the rule for independent events and conditional probability | P(A|B)=P(A|B')=P(A) |

P(A)+P(B)-P(A∩B)= | P(A∪B) |

(P(B∩A))/(P(A))= | P(B|A) |

What are the probability symbols for and and or | And=∩ Or=∪ |