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Apr. 23 Statistic for the day: Chance that a woman first elected to the U.S. house or senate before 1993 was a congressional widow: 1 in 4 Assignment: Read Chapter 24 Do exercises 1, 6, 8, 9, 10 These slides were created by Tom Hettmansperger and in some cases modified by David Hunter

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Variable Sex N Mean StDev SE Mean Credits Female Male Fastcar Female Male Cigpacks Female Male Research question: Do males and females in Stat 100 differ with respect to average credits? Null: They do not differ Alternative (2-sided): They differ 2-sided p-value: 2(.11) =.22 Decision: WE HAVE NO EVIDENCE OF A DIFFERENCE.

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Variable Sex N Mean StDev SE Mean Credits Female Male Fastcar Female Male Cigpacks Female Male Research question: Do males and females in Stat 100 differ with respect to average fastest speed driven? Null: They do not differ Alternative (2-sided): They differ 2-sided p-value: (Off the chart!) Less than 2(.0001) =.0002 Decision: WE HAVE STRONG EVIDENCE THAT MEN HAVE DRIVEN FASTER ON AVERAGE.

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Variable Sex N Mean StDev SE Mean Credits Female Male Fastcar Female Male Cigpacks Female Male Research question: Do males and females in Stat 100 differ with respect to average cigarette packs per day? Null: They do not differ Alternative (2-sided): They differ 2-sided p-value: About 2(.005) =.01 Decision: WE HAVE EVIDENCE THAT MEN SMOKE MORE.

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Research question: Do yellow M&M’s really occur in the proportion claimed on the M&M’s website? ColorClaimed Count in sample Yellow Blue Green (Counts come from a representative sample of size 5533.) Null: True proportion =.14 Alternative (2-sided): True proportion ≠.14 Sample proportion: 783/5533 = sided p-value: 2(.33) =.66 Decision: WE HAVE NO EVIDENCE THAT YELLOW M&M’s DIFFER FROM THE PROPORTION CLAIMED.

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Research question: Do blue M&M’s really occur in the proportion claimed on the M&M’s website? ColorClaimed Count in sample Yellow Blue Green (Counts come from a representative sample of size 5533.) Null: True proportion =.24 Alternative (2-sided): True proportion ≠.24 Sample proportion: 1280/5533 = sided p-value: 2(.06) =.12 Decision: WE HAVE NO EVIDENCE THAT BLUE M&M’s DIFFER FROM THE PROPORTION CLAIMED.

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Research question: Do green M&M’s really occur in the proportion claimed on the M&M’s website? ColorClaimed Count in sample Yellow Blue Green (Counts come from a representative sample of size 5533.) Null: True proportion =.16 Alternative (2-sided): True proportion ≠.16 Sample proportion: 803/5533 = sided p-value: About 2(.0013) =.0026 Decision: WE HAVE STRONG EVIDENCE THAT THE PROPORTION OF GREEN M&M’s IS SMALLER THAN.16.

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Return to chi-squared statistics Suppose we are interested in the following research question: Is there a significant difference between men and women in STAT 100 with respect to the prevalence of body piercing? According to the survey for this class, 28.57% of women (out of 135) versus 5.56% of men (out of 99) have body piercings.

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Rows: gender Columns: body pierces top lines of numbers are observed bottom lines are expected no yes All female male All

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How to measure the distance between what the research advocate observes in the table and what the skeptic expects: Add up the following for each cell:

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But our chi-squared is so the research advocate easily wins! There is a statistically significant difference between men and women. Chi-squared distribution with 1 degree of freedom: If chi-squared statistic is larger than 3.84, it is declared large and the research advocate wins.

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How about a p-value for the body piercing test? The key is to take the square root of the chi-squared statistic and treat that as the standardized score! Null: No difference between men & women Alternative (2-sided): A difference exists 2-sided p-value: (Off the chart!) Less than 2(.0001) =.0002 Decision: WE HAVE STRONG EVIDENCE THAT WOMEN HAVE BODY PIERCINGS MORE OFTEN THAN MEN.

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Rows: gender Columns: cell phone no yes All female male All Exercise : Follow the 4 steps and answer the Research Question: Is there a relationship between gender and ownership of cell phones in Stat 100.2? Data

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