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Final-formulachart.pptxFormula Sheet
Basic Practice of Statistics
7th Edition
1
| Sample | Population | |
| size | ||
| Notation for mean | ( read “x-bar”) | ( read “miu”) |
| Formula for the mean |
2
Weighted Mean
Outliers:
3
Standard Deviation
| Sample | Population | |
| Size | ||
| Notation | ||
| Formula | ||
| Simple formula for calculation |
4
Variance
| Sample | Population | |
| Size | ||
| Notation | ||
| Formula for variance | ||
| Formula for calculation |
5
Empirical Rule
6
Chebyshev’s Theorem
7
Z - Score
| Sample | Population | |
| mean | ||
| Standard deviation | ||
| Formula for Z-score |
8
Formula for the sample linear correlation coefficient
9
Testing for Correlation in the population
10
11
12
Slope and y-intercept of the regression Equation
13
Complementary Events
Addition Rule:
Independent events and multiplication Rule
When two events A and B are said to be independent, then
Dependent events and multiplication Rule
When two events A and B are dependent, let
= probability that B occurs assuming (given) that A has already occurred
Conditional Probability
Parameters of a Discrete Probability Distribution: Mean, Variance, and standard deviation
Note:
| Parameter | Formula |
| Mean | |
| Standard Deviation | |
| Variance |
Expected Value for a discrete random variable
The expected value (E) of a discrete random variable is the mean of the probability distribution of x. That is,
Permutation Formula
The number of permutations of n objects taking r at a time
Combination Formula
The number of combinations of n objects taking r at a time is denoted or where
Or
Binomial Distribution
The number of successes in the n trials is a discrete random variable. That is, values of x are :
The probability distribution of is called a binomial distribution with parameters .
, where
Mean, Variance, Standard Deviation of a Binomial Distribution.
Let n be the number of trials in a binomial procedure, and let
p = P(Success) = probability of success and
q =1 – p = P(Failure)
The mean number of successes in n trials
µ = np
The variance
Standard Normal Distribution
25
Critical values Notation
is the z-score with corresponding area to the right α.
Transformation form , to
Normal Approximation for Binomial Distributions
Given has binomial distribution with observations and success probability p. When is large, the distribution of is approximately Normal
Transforming the values of to z-scores
Using the idea of
z = . Given that = µ, and = , then z = =
Formula for a confidence interval for population mean is
| or |
Critical values for the confidence interval for Z-distribution
Summary: Confidence interval for the population mean µ when σ is known
σ is known
We find critical values and using the standard normal distribution
We find Margin of error
We find
Sample size for confidence intervals when is known
Size of the sample required to achieve the level of confidence.
Round up the results to the next whole number.
Critical values for the confidence interval for Z-distribution
Summary: Confidence interval for the population mean µ when σ is unknown
σ is unknown
We find critical values and using the
Table C
We find Margin of error
df = n - 1
We find
Confidence interval for true population proportion p
Recall: the sampling distribution of the sample proportion is normally distributed. That is
where
| Parameter | Best Point Estimates | |
| Proportion | (population proportion) |
Confidence interval for true population proportion p
We find critical values and using the
Table A
We find Margin of error , where
We find
Test Statistic for testing hypothesis for population mean µ
: µ=,
: µor : µ or : µ
| known | unknown | |
| Test Statistic | , : µ= | , : µ= |
| . | . | |
| , |
Test Statistic for testing hypothesis for population proportion
: p=,
: por : p or : p
| Test Statistic | , |
| : p= , | |
| , |
P-value for Z-distribution
Testing for population mean when is known or
Testing hypothesis for the population proportion
Method1: We use the p-value
For : µ(left tailed test or one sided test)
: µ(two tailed test or two sided test)
Decision making in hypothesis testing for the population mean when is unknown.
Recall: When is unknown we have t-distribution.
Method1: We use the p-value
For : µ(left tailed test or one sided test)
: µ(two tailed test or two sided test)
