STATISTICS: The BIG Picture Jim Bohan Manheim Township School District pa.us.

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Presentation transcript:

STATISTICS: The BIG Picture Jim Bohan Manheim Township School District pa.us

The Statistics Store We can “prove” anything you want!

The Statistical Process

Design l Surveys l Observational Studies l Controlled Experiments

Descriptive Statistics One Variable l Graphs stem plots box plots histograms dot plots l Numerical Summaries mean and standard deviation five number summary

Descriptive Statistics Two Variables l Graph scatter plot l Numerical Summaries correlation: linear association regression/residuals: prediction

Inferential Statistics: The Concept sampling Population Sample (parameter) (statistic) inference

Inferential Statistics: The Foundation l Probability l Probability Distributions l Sampling Distributions

Inferential Statistics: The Techniques l Estimation of a parameter: Confidence Intervals l Testing of a parameter: Tests of Significance

An Example Pose the question: The principal of a large high school wishes to determine the mean number of hours that her students do homework per week.

Gather Data l The principal asks the Chair of the Mathematics Department to conduct a simple random sample of the students. l The Math Chair determines that a simple random sample of 35 will be sufficient.

Organizaton and Analysis - the results l n = 35 l Mean = 7.24 l SD = 2.65

Interpretation We wish to estimate the mean number of hours for the entire student body. Therefore, we will calculate the 95% Confidence Interval. Criteria: 1. Simple Random Sample: done 2. n > 30: n =35

The Estimate Since the criteria are satisfied: The 95% t-Confidence Interval is (6.33, 8.15) Therefore, the principal should be 95% confident that the mean number of hours of homework for the entire student body is within this interval.