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

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.

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.

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.

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.

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.

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.

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.

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

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:

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.

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.

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