Math 130 Day 16 summary.pdf

# Math 130 Day 16 summary.pdf - Sec 10.1 Introduction to...

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Sec. 10.1: Introduction to Hypothesis Tests Sec. 10.3: Hypothesis Tests for a Population Mean 𝜇

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Idea Behind Hypothesis Tests (for ) 𝜇 To settle the dispute… 1. Take a sample (only one) 2. Calculate 𝑥 If , believe the king If , believe the king If , it depends! If but close to 20, still believe the king If but far from 20, then believe the peasant 𝑥 = 20 𝑥 > 20 𝑥 < 20 𝑥 < 20 𝑥 < 20
How Do You Tell If 2 Numbers Are “Close Together” Or “Far Apart”? Question : Are the numbers 10 and 14 “close together” or “far apart”? Answer: It depends on the standard deviation !!! 𝜎 If , then 10 and 14 are 2 steps away and so they are close together. If , then 10 and 14 are 8 steps away and so they are far apart. 𝜎 = 2 𝜎 = 0.5

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How Can You Tell How Many “Steps” Apart 2 Numbers Are? Answer : That’s what the z transformation formula tells you!! 𝑍 = 𝑋 − 𝜇 𝜎 Ex: If the mean of a bunch of numbers is and the standard deviation of those numbers is , a) How many steps away is the data point from the mean? b) What does the sign of the answer in part (a) mean?
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