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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 136 15.566 2.073 0.178 Male 100 15.250 1.833 0.183 Fastcar Female 134 91.5 14.92 1.29 Male 98 108.4 23.88 2.41 Cigpacks Female 136 0.419 1.227 0.105 Male 101 1.108 2.300 0.229 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 136 15.566 2.073 0.178 Male 100 15.250 1.833 0.183 Fastcar Female 134 91.5 14.92 1.29 Male 98 108.4 23.88 2.41 Cigpacks Female 136 0.419 1.227 0.105 Male 101 1.108 2.300 0.229 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 136 15.566 2.073 0.178 Male 100 15.250 1.833 0.183 Fastcar Female 134 91.5 14.92 1.29 Male 98 108.4 23.88 2.41 Cigpacks Female 136 0.419 1.227 0.105 Male 101 1.108 2.300 0.229 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.14783 Blue.241280 Green.16803 (Counts come from a representative sample of size 5533.) Null: True proportion =.14 Alternative (2-sided): True proportion ≠.14 Sample proportion: 783/5533 =.142 2-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.14783 Blue.241280 Green.16803 (Counts come from a representative sample of size 5533.) Null: True proportion =.24 Alternative (2-sided): True proportion ≠.24 Sample proportion: 1280/5533 =.231 2-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.14783 Blue.241280 Green.16803 (Counts come from a representative sample of size 5533.) Null: True proportion =.16 Alternative (2-sided): True proportion ≠.16 Sample proportion: 803/5533 =.145 2-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 84 51 135 103.85 31.15 135.00 male 96 3 99 76.15 22.85 99.00 All 180 54 234 180.00 54.00 234.00

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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 38.85 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 12 124 136 male 14 87 101 All 26 211 237 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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