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The topics covered are from chapters 1-13 and covers topics of probability, hypothesis tests, different types of distributions, etc. It's not a stand-alone sheet, but it has some good information, which is helpful when answering questions. I hope it helps!
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Stats final review Ch. Statistics can be broken into: (1) descriptive (summarize info from samples), (2) inferential (methods that take data from samples and make generalisations about a population) Simple random sample- (use table 1) Ch. 2 & 3 Data can be broken into (1) categorical and (2) numerical where (2) can be broken further into (a) discrete (single number) and (b) continuous (numbers from an interval that includes decimals) Frequency tables can be used to summarize data Example of frequency table: M F Frequency (f) 2 2 Relative frequency (r.f.) 0.5 0. Graphical methods to summarize numerical data: histogram, boxplot, stem and leaf diagram, dotplot Numerical methods to summarize data: Describe centre: mean, median, mode Describe spread: standard deviation, Interquartile range, range Ch. 4 f/N rule: rule that states the probability of a simple event happening is simply the number of times the event can happen (frequency/ the number of possible times an event can happen) Properties of probability:
Conditional probability- probability that event A occurs if event B occurs Denoted as P(A|B) ≠ P(B) Conditional probability rule- given the intersection of events A and B and the probability of B the conditional probability of A given B is: P(A|B) = P(A&B)/ P(B) Two events A and B are independent if one of the following holds true:
Ch. Normal random variable = continuous random Normal distribution = bell shaped A normal random variable with mean 0 and standard deviation 1 is called a standard normal random variable… is denoted as Z The distribution is called a standard normal distribution Standardizing: (transforming to a standard normal random variable…this finds the Z value) The area to the left of a-𝜇/𝝈 (aka p-value which is the probability) can be found using table 2 The area to the right of a-𝜇/𝝈 can be found using table 2 then do 1 - P since the table finds the area to the left The total area under the standard normal density curve is 1 Ch. Sampling distribution of the sample mean- for a sample of size n, the sample mean will behave accordingly to this distribution Distribution types:
Assuming that the random variable X has mean μ and standard deviation 𝝈, then the mean of x̄ of samples with sample size n is still μ. The standard deviation of x̄ of samples with sample size n is 𝝈/⇃n Sampling error- the difference between the sample mean and the population mean Ch. Given a SRS with sample size n a (1-a) 100% confidence interval for the population mean is: From x̄- Za/2 ・ 𝝈/⇃n to x̄- Za/2 ・ 𝝈/⇃n Margin of error =the c length (half the length of the interval) If the population standard deviation is unknown then when can use the sample standard deviation (denoted as s) From x̄- ta/2 ・ s/⇃n to x̄- ta/2 ・ s/⇃n Ch. Hypothesis testing errors:
Significance level and assumptions (all expected frequencies are at least 1, at most 20% expected frequencies are less than 5, SRS) Use X^2 table to find critical values/ p value Chi square independence test: Ho: two variables are not associated Ha: two variables are associated If two variables are not associated the expected proportion of each cell should be equal to R/n x C/n (row/ number of values in the row x column/ number of values in the column)