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What is the symbol for the population mean?
μ (mu) is the symbol for the population mean, which is constant value.
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What is the symbol for the sample mean?
 (xbar) is the symbol for the sample mean, which is variable and changes depending on the sample used.
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What is the symbol for the population standard deviation?
is the symbol for the population standard deviation
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What is the symbol for the sample standard deviation?
S is the symbol for the sample standard deviation
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What is the symbol for the population variance?
2 is the symbol for the population variance
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What is the symbol for the sample variance
S2 is the symbol for the sample variance
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A piece of information about population data is known as a what?
Parameter
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A piece of information about sample data is known as a what?
Statistic
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What is the relationship between a population and a sample?
A sample is part of, and is representative of a population
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What is the mean a measure of?
Central tendancy/location
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What is the median a measure of?
Central tendency/location
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What is the mode a measure of?
Central tendency/location
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What are the four measures of variability?
- Range
- Variance
- Standard deviation
- Coefficient of variation
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What is the equation for the population mean?
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What is the equation for the sample mean?
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What is the range?
Range = Largest measurement - smallest measurement
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What is the median?
The value that falls in the middle when the values are arranvged in sequential order (or an 'ordered array')
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What can the mean, median and mode tell you about the distribution of a data set?
- All equal =symmetrical
- Mean > median = positively skewed
- Mean < Median = negatively skewed
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What does the variance measure?
Dispersion
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What is the standard deviation?
The square root of the variance, and a measure of dispersion. It allows for the comparison of the variability of several distributions and make a statement about the general shape of a distribution
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What does the correlation coefficient indicate?
The strength of the linear relationship between two variables
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What is the coefficient of variation?
A method of measurement that provides a proportionate measure of variability
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What is a conditional probability?
The probability of an event when partial knowledge about the outcome of an experiment is P(A|B) = the conditional probability that event A occurs, given that event B has occurred.
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If we are calculating 'greater than' (>) probabilities, can we find it directly from the z-tables, or must we subtract from 1?
If we are calculating '>' we will subtract from 1
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If we are calculating 'less than' (<) probabilityies, can we find it directly from the z-tables, or must we subtract from 1?
If we are calculation '<' we can find it directly from the z-tables.
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What does represent in Poisson Probability?
Both the mean and the variance
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When is the Poisson Probability used?
When we are interested in the probability of the number of events in a given interval (e.g. could be a time frame)
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How do we determine if the parameter of interest is qualitative?
The question includes words, or percentage or proportion
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How do we determine if the parameter of interest is quantitative?
The question includes number, average or mean
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What is statistical inference?
The process of drawing conclusion about properties of a population based on information obtained from a sample
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What factors affect sampling error?
- The sample size: we want it to be large
- The variance of the sample values: If the sample values vary greatly, the sampling error may be large, and it is difficult to make an inference about the population
- The variability of the population itself: can't control this but can reduce the sampling error by increasing the sample size
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What are sampling errors?
The difference between the sample mean and the population mean, due to the selected sample. It is expected to occur when making a statement about the population based on the sample taken
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What is the Z /2 value when the confidence level is 90%?
1.645
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What is the Z /2 value when the confidence level is 95%?
1.96
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What is the Z /2 calue when the confidence level is 98%?
2.33
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What is the Z /2 value when the confidence level is 99%?
2.575
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If H0 is true but you reject H0, has an error been made?
You have made a Type I Error
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If H0 is true and you do not reject H0, has an error been made?
No, the correct decision has been made
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If HA is true and you do not reject HO, has an error been made?
You have made a Type II Error
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If HA is true and you reject HO, has an error been made?
No, the correct decision has been made
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If the p-value < , do we reject or not reject?
Reject
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If the p-value > , do we reject or not reject?
Cannot reject
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How do we interpret the p-value?
We can conclude that the smaller the p-value the more statistical evidence exists to support the alternative hypothesis
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What does the p-value tell us?
It provides information about the amount of statistical evidence that supports the alternativ hypothesis. The p-value of a test is the probability of observing a test statistic at least as extreme as the one computed, given the the null hypothesis is true
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What is the mean standard error of estimate equal to?
0
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If the is small, what can we infer?
It means that the errors tend to be close to 0 (close to the mean error), and therefore the model fits the data well. Therefore, we can use sigmaepsilon as a measure of suitability of using a linear model.
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What does 0, the y-intercept, tell us?
It tells us the expected value of y, when x=0
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What does 1, the gradient/slope, tell us?
The expected change (increase/decrease) in y (positive/negative) for every unit increase in x
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What does p-hat equal?
X/n
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REMEMBER TO INCLUDE THE alpha/2 in immediately following BOTH t and Z..
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What is the impact of outliers?
- Very small values make xbar smaller than the median
- Very large values make xbar larger than the median
- Either very small or very large values make S^2 and S larger
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What do Z-scores tell us?
Z scores show the difference between x and mu measured in standard deviations
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How do we interpret r?
- When r is close to -1, we have a strong negative relationship
- When r is close to +1, we have a strong positive relationship
- When r is no to 0 we have no relationship
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If r2 = 0.83, what does this mean?
83% of variation in y can be explained by variation in x
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How do we interpret Se or Sxy?
If we have two models with the same Y variable and a different X variable then the model with the smaller Se or Sxy is said to be better as it has smaller residuals.
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The possible phat values have a normal distribution if...?
(n)(p-hat)>5 and n(1-(p-hat)>5
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What does p-hat equal?
x/n
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What is the p-value?
The probability we get a sample with this or a more extreme value when H0 is true
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What is classical frequency?
Each outcome has the same chance of occuring. It is the ratio of the number of ways "a" can occur and the number of possible outcomes.
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What is relative frequency?
When a situation is repeated e.g. customers walk into a shop. If "a" is the event or outcome that a person buys a fruit juice, the frequency is the ratio of the number who by and the total number of customers.
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What is subjective frequency?
In thos situations where we do not know all the outcomes, the outcomes may not be equally likely, we are not able to repeat the situation e.g. each repair job may be different from all other repair jobs, we use the subjective approach where P(A) is a value between 0 and 1 which reflects the subjective feelings of a decision make about the chance "A" will occur
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