DO NOW

´ Find your number in the lists posted in the bulletin boards (back wall and main entrance).

´ Find the seat with your number and that will be your seat from now on.

´ SILENCE YOUR PHONE and put it in the pocket that has your number in the bulletin board (back wall).

´ NO EXCEPTIONS and NO PHONES in backpack. If I see your phone, I will take it!!!

´ No food or drinks (except water) allowed in my room. Finish your food outside before you enter my classroom.

Semester Exam Review Topics and Techniques

Units coveredUnit 1: Data CollectionUnit 2: Organize and Summarize DataUnit 3: Normal Probability DistributionsUnit 4: Confidence Intervals

Unit 1: Data Collection

´ Descriptive statistics vs. Inferential statistics

´ Population vs. Sample´ Parameter vs. Statistic

´ Proportions

´ Categorical Data vs. Quantitative Data´ Quantitative – Discrete

´ Quantitative - Continuous

Unit 1: Data Collection

´ Sample Surveys

´ What are the goals?

´ What is the targeted population?

´ What questions will be asked?

´ How will the participants be selected?

´ How will the data be analyzed and presented?

´ Sources of Bias in Sampling and Surveys

´ Undercoverage

´ Nonresponse bias

´ Response bias

´ Sampling Techniques That Create Bias

´ Voluntary response sample

´ Convenience sample

Unit 1: Data Collection

´ Sampling Methods ´ Simple random sample (SRS)´ Stratified random sampling

´ Systematic random sampling

´ Cluster random sampling ´ Multistage random sampling

´ Experiments vs. Observational Studies ´ Observational can be retrospective or prospective

´ Experiment has experimental units, response variables and factors (by levels and treatments)

Unit 1: Data Collection

´ Three Principles of Experimental Design ´ Control

´ Blind

´ Double Blind

´ Placebo

´ Randomization´ Completely randomized

´ Block design

´ Matched pair design

´ Replication

´ Lurking and Confounding Variables´ Lurking variable – A variable that is not! Incorporated into the design of a research

study ´ Confounding variable – A variable that is incorporated into the design of a research

study

´ Generalizability of Results and Conclusions

Unit 2: Organizing and Summarize Data

´ Frequency and Relative Frequency Tables

Unit 2: Organizing and Summarize Data

´ Joint Frequency Tables

´ Marginal Frequencies

´ Marginal Relative Frequencies

´ Conditional Frequencies

Unit 2: Organizing and Summarize Data

´ Pie Chart

Unit 2: Organizing and Summarize Data

´ Bar Chart

Unit 2: Organizing and Summarize Data

´ Comparing Distributions

Unit 2: Organizing and Summarize Data

´ Frequency Tables for Quantitative Data

Unit 2: Organizing and Summarize Data

´ Dot Plot

Unit 2: Organizing and Summarize Data

´ Stemplots

Unit 2: Organizing and Summarize Data

´ Histograms

Unit 2: Organizing and Summarize Data

´ Box Plot

´ Outliers´ IQR*1.5

´ Add that to Q3

´ Subtract that from Q1

Unit 2: Organizing and Summarize Data

´ Measures of Center´ Mean

´ Median

´ Mode

´ Measures of Spread´ Standard Deviation (and variance)

´ Interquartile Range

´ Range

Unit 2: Organizing and Summarize Data

Unit 3: Normal Probability Distributions

34%34%

68%

47.5%47.5%95%

49.85%49.85%99.7%

Unit 3: Normal Probability Distributions

´ Empirical Rule

68% of the data values fall within 1 standard deviation of the mean in either direction

95% of the data values fall within 2 standard deviation of the mean in either direction

99.7% of the data values fall within 3 standard deviation of the mean in either direction

Remember values in a data set must appear to be a normal bell-shaped histogram, dotplot, or stemplot to use the Empirical Rule!

Unit 3: Normal Probability Distributions

Unit 3: Normal Probability Distributions

Central Limit Theorem

1. The distribution of means will be approximately a normal distribution for larger sample sizes

2. The mean of the distribution of means approaches the population mean, µ, for large sample sizes

3. The standard deviation of the distribution of means approaches for large sample sizes, where σ is the standard deviation of the population and n is the sample size

σ/ n

Unit 3: Normal Probability Distributions

Unit 3: Normal Probability Distributions

´ BinomialDistribution´𝑝 is probability of success on an individual trial´𝑞 is probability of failure on an individual trial´𝑛 is the sample size´𝜇 is the mean (average)´𝜎 is the standard deviation´ If 𝑛𝑝 ≥ 5 and 𝑛𝑞 ≥ 5, then the normal distribution can be

used for approximation.

Unit 4: Confidence Intervals

´ Confidence Intervals for the Mean when 𝜎 is known.´ The population standard deviation (𝜎) is given, the sample size (𝑛) is given and

they will give you a 90%, 95% or 99% confidence, so you will use 1.65, 1.96 or 2.58 as your z-scores. So, you will use 𝐸 = 𝑧 9

:�to find the maximum error of the

estimate and then subtract from and add to the mean or point estimate.

Unit 4: Confidence Intervals

´ Determining sample size for regular data (not proportions)´ You need the maximum error of the estimate, the population standard deviation,

and the degree of confidence.

Unit 4: Confidence Intervals

´ Confidence Intervals for the Mean when 𝜎 is unknown.´ The SAMPLE standard deviation (𝑠) is given, the sample size (𝑛) is given.

´ You will need to find a 𝑡 score.

´ Determine the degrees of freedom 𝑑 = 𝑛 − 1

´ They will give you a % of confidence and you will match the degrees of freedom with the % of confidence.

´ Then, you will use 𝐸 = 𝑡 A:�

to find the error and subtract from and add to your mean.

Find the 𝒕𝜶/𝟐 value for a 95% confidence interval when the sample size is 22.

Unit 4: Confidence Intervals

´ Confidence Intervals and Sample Size for Proportions´ When the information given is in proportions, you need to use other methods to

find the confidence interval. ´ To construct a confidence interval about a proportion, you must use the

maximum error of the estimate, which is

´ When you find 𝐸 you add it to and subtract it from the proportion.´ Rounding Rule for a Confidence Interval for a Proportion Round off to three

decimal places.

𝑬 = 𝒛𝒑I𝒒I𝒏

�

Unit 4: Confidence Intervals

´ To find the sample size needed to determine a confidence interval about a proportion, use this formula:

𝒏 = 𝒑I𝒒I𝒛𝜶/𝟐𝑬

𝟐

Where do I practice? ´ Questions will be taken from your End-of-Unit Exams, so YOU SHOULD START

THERE!!!´ Go to Khan Academy: https://www.khanacademy.org/

´ Click on “Learners Start Here.”

´ Click on “Statistics and Probability.”