Docsity
Docsity

Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity


Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan


Guidelines and tips
Guidelines and tips

This doc was used for my open book final test for Stats 151. Has good summaries..., Study notes of Business Statistics

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!

Typology: Study notes

2020/2021

Uploaded on 12/11/2023

jackson-weekes
jackson-weekes 🇨🇦

1 document

1 / 7

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
Stats final review
Ch.1
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
0.5
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:
1. The probability of an event is between 0 and 1
2. The probability that isn’t possible is 0
3. The probability that always happens is 1
Complement rule: P(not A)= 1 - P(A)
Addition rule: P(A) + P(B) - P(A&B)
Mutually exclusive- no common sample points in A and B
If A and B are mutually exclusive:
P(A&B) = 0 and P(AorB) = P(A) + P(B)
pf3
pf4
pf5

Partial preview of the text

Download This doc was used for my open book final test for Stats 151. Has good summaries... and more Study notes Business Statistics in PDF only on Docsity!

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:

  1. The probability of an event is between 0 and 1
  2. The probability that isn’t possible is 0
  3. The probability that always happens is 1 Complement rule: P(not A)= 1 - P(A) Addition rule: P(A) + P(B) - P(A&B) Mutually exclusive- no common sample points in A and B If A and B are mutually exclusive: P(A&B) = 0 and P(AorB) = P(A) + P(B)

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:

  1. P(A|B) = P(A)
  2. P(B|A) = P(B)
  3. P(A&B) = P(A) x P(B) Finding the probability of the intersection of two events: (joint probability) Conditional probability rule: P(A&B) = P(A) x P(A|B) If A and B are independent and their marginal probabilities P(A) and P(B) are known then the joint probability of A and B is: P(A&B) = P(A) x P(B) If the marginal probabilities of A and B are known, and the probability of the union P(AorB) are known, then according to the additional rule the joint probability of A and B is: P(A&B) = P(A) + P(B) - P(AorB) Basic counting rule (with stage 1 = m and stage 2 = n) there are mn outcomes Combination: (the number of possible combinations of r objects from m objects) 𝑚𝐶𝑟 = 𝑚! /𝑟! (𝑚 − 𝑟)! Permutation: (order selected matters, permutation of r objects from a collection of m objects) 𝑚𝑃𝑟 = 𝑚! / (𝑚 − 𝑟)! Ch. Discrete random variable- a random numerical variable that takes on distinct numbers (like 0, 1, 2, 3 …) Continuous random variable- a random variable that can take on infinitely many values Table to summarize discrete random variables: Example: number of children a selected family has Possible values (X) 0 1 2 Probability (P(X=x) 0.1 0.25 0. Population mean of a discrete random variable X:

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:

  1. Normal: (bell shaped)
  2. Approximately normal (example: asymmetric, not unimodal, large sample)
  3. Not normal (example: asymmetric, not unimodal, small sample) Central limit theorem (CLT): the sample mean is approximately normally distributed for a relatively large sample size, regardless of the parent distribution For a skewed population n=30 will be enough to apply the CLT For a severely skewed population n=100 or even n=500 will be necessary to apply the CLT

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:

  1. Type 1 error: Ho is rejected when Ho is actually true
  2. Type 2 error: Fail to reject Ho when Ho is not true Steps in hypothesis testing:
  3. Ho: (opposite of Ha, always has an equal sign) Ha: (μ≠μo or μ>μo μ<μo)
  4. Significance level (risk of making type one error) and assumptions (SRS, x̄ is normal or approximately normal)
  5. Test statistic value (to= x̄-μo/ s/√n)
  6. Find the critical values (and the rejection region(s)) or the p value
  7. Determine whether the null hypothesis (Ho) is rejected
  8. Make an english conclusion statement Ch. Two methods for hypothesis testing with two population means:
  9. Independent t test: The two samples are independent samples, sample sizes could be equal or unequal
  10. Paired t test: If n selected is the same for both populations they are called paired samples because the observation in the first sample is related to an observation in the second sample (paired samples have the same sample size) Independent t test: (non-pooled t test) Step 1: Ho: μ1- μ2=0 or μ1- μ2=>0 or μ1- μ2<=μo Ha: μ1- μ2≠0 or μ1- μ2<0 or μ1- μ2>μo

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)