# Essay on MATH 159

Submitted By laynah
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Exam 2 Study Guide - Math 159
Term / Concept
Alternative Hypothesis择一假设（8）
“What you suspect is true”
Always stated in terms of a population parameter A statement that the population parameter
(e.g. mean, proportion, standard deviation)
Somehow differs to some claimed value
ANOVA方差分析（cheapter12）
ANOVA Definition
A hypothesis假设 test for comparing the equality of 2 or more means
Alternative Hypothesis: at least one mean is different from the others
Null Hypothesis: the means are equal

Bartlett's Hypothesis Test(12)
1. Each sample (column) of data is~ Normally Distributed
2. Populations have ~ equal variances
Bartlett’s Test (Bartlett’s Hypothesis Test for comparing multiple variances)

As long as the smallest variance is not more than 9 time smaller than the largest variance, OK
3. Sample (columns) are simple random samples
4. Sample (columns) are independent
5. Sample (columns) are have~=samples sizes (n)

Binomial Distribution二项分布（5）
A specific type of discrete probability distribution that meets these 4 requirements:
1. the process has a fixed # of trials/events
2. The trials/events must be independent of each other
3. Each outcome must have two and only two possible outcomes
Commonly labelled “success” and “failure”
4.The probability of a “ success” remains the same across all process trials/events的可能性是相同的“成功”在所有流程试验/事件

Central Limit Theorem（6）
The distribution of sample means样本的分布方式 will always be normal in shape
Assuming sample size, n 30
Mean of the Sample Means =
The St. Dev. of the Sample Means =

Chi Square Hypothesis Test(8)

Confidence Interval one of 3 tools of statistical inference统计推断
A range of values ( an interval) from a random sample used to estimate the true unknown population parameter (
Think of a “fisherman’s net”
Example:
“52% is an example of a confidence interval for the population of those that will vote for me

Confidence Level of a Confidence Interval
The “success rate” of the confidence interval calculation process
Overlaps the true parameter of interest (1- of the time
Typical confidence interval levels are 95%, 99% and 90%

accuracy “nearness to truth” “nearness to the parameter how close is your statistic (estimate) to the five value (parameter)

Reliability “repeatability’ long term success vote ( confidence level) of your process
Precision how close together your measurements are typically measure with standard error =harrow CI

Expected Value of a Probability Distribution概率分布 mean of a probability distribution
Represents the average of all the potential outcomes代表平均的所有潜在的结果 it is average value we would expect to get if the trials could continue indefinitely这是平均值我们期望得到如果试验可以无限期地持续下去
Also know as the “Expected Value” and is denoted by E
Formula: E= of the probability distribution

Hypothesis Test假设检验
A tool of statistical inference used when you want to make a statement or decision about a population parameter using a random sample 当你想要使用一个语句或决定对人口参数使用随机样本 can be performed for any population parameter using a random sample可以执行任何总体参数使用随机样本 also called “ Significance Tests显着性检验”

Inferential Statistics推论统计学
Make inferences, or generalizations概括；一般化, about a population. using random sample statistics to estimate population parameters
Margin of Error误差幅度；误差界限

Abbreviated as “E”
The “ part of the 52% 2%

A quantification定量，量化 of the expected error in using the sample statistic to estimate the population parameter一个量化预期的错误在使用示例统计估计人口参数
The maximum likelihood difference with probability (1 –) between the observed sample statistic观察样本统计 and the true population parameter