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What is statistics? “Statistics is the study of the collection, organization, analysis, and interpretation of data.”
How tall are students in this class? How can we answer this question? What data would you need to collect?
How tall are students in this class? MEAN: Mean = 69.30
How tall are students in this class? S = 4.84 STANDARD DEVIATION:
Mean = 8.88 Std Dev = 1.90 Mean = 9.02 Std Dev = 3.77
How tall are students in Michigan? How can we answer this question? Would you need a different sample compared to our previous question?
How tall are students in Michigan? STANDARD ERROR: SE = 0.80
Are students in Michigan taller than students in Ohio?
SQUARED! Half the class gets bean type 1, half the class bean type 2 Do the two types of beans have different lengths?
MEAN: STANDARD DEVIATION: STANDARD ERROR:
Discussing the student measurements of building height. Letting them originate concepts for: Multiple measures Mean Standard Deviation Outliers / identifying.
There are two statistical tests for mean: 1) z test – Used for large samples (n ≥ 30) 1) t test – Used for small samples (n < 30)
T T Population Sample Size Calculations Purpose Allows the analyst to analyze the sample size necessary to conduct "statistically significant"
1 Finding Sample Variance & Standard Deviation Given: The times, in seconds, required for a sample of students to perform a required task were: Find:
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Squaring of a number ending in 5 An approach to determine answers Quickly! Squaring of a number ending in 5.
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Starter The length of leaves on a tree are normally distributed with a mean of 14cm and a standard deviation of 4cm. Find the probability that a leaf is:
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$100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300.
Distribution of the Sample Mean (Central Limit Theorem)
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Rebecca Robinson. Listed all public universities in the United States and numbered them. Used a random number generator to generate 25 random colleges.
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5 ft 3ft 5ft 3ft Always write your answer with the unit of measurement.
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Multiplication X 1 1 x 1 = 1 2 x 1 = 2 3 x 1 = 3 4 x 1 = 4 5 x 1 = 5 6 x 1 = 6 7 x 1 = 7 8 x 1 = 8 9 x 1 = 9 10 x 1 = x 1 = x 1 = 12 X 2 1.
Division ÷ 1 1 ÷ 1 = 1 2 ÷ 1 = 2 3 ÷ 1 = 3 4 ÷ 1 = 4 5 ÷ 1 = 5 6 ÷ 1 = 6 7 ÷ 1 = 7 8 ÷ 1 = 8 9 ÷ 1 = 9 10 ÷ 1 = ÷ 1 = ÷ 1 = 12 ÷ 2 2 ÷ 2 =
Comparison of Two Means Paul Niezguski Peter Heisler University of Michigan College of Engineering.
Confidence Intervals Mon, March 22 nd. Point & Interval Estimates Point estimate – use sample to estimate exact statistic to represent pop parameter.
BCOR 1020 Business Statistics Lecture 28 – May 1, 2008.
Statistics Estimates and Sample Sizes Chapter 7, Part 2 Example Problems.
1 How do we interpret Confidence Intervals (Merit)? A 95% Confidence Interval DOES NOT mean that there is a 95 % probability that the population mean lies.
Vocab Normal, Standard Normal, Uniform, t Point Estimate Sampling distribution of the means Confidence Interval Confidence Level / α.
THE CENTRAL LIMIT THEOREM The World is Normal Theorem.
MATH IN THE FORM OF STATISTICS IS VERY COMMON IN AP BIOLOGY YOU WILL NEED TO BE ABLE TO CALCULATE USING THE FORMULA OR INTERPRET THE MEANING OF THE RESULTS.
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Randomization and Bootstrap Methods in the Introductory Statistics Course Kari Lock Morgan Robin Lock Duke University St. Lawrence University
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