Chi-Squared Hypothesis Testing
Find the expected cell count for men who prefer romance films
Documentary Horror Romance
Men 10 20 40
Women 35 15 30
32.67
Delta has 500 songs downloaded to her phone, and she wants to estimate what proportion of the songs are by a female artist. She takes an SRS of 50 songs on her phone and finds that 20 of the songs sampled are by a female artist.
What is the equation we want to use?
statistic +/- z* (the square root of) ((p-hat (1-p-hat)) / n
What is a population?
The complete set of people
"All (persons, things, places, etc.)"
100 GVSU freshman were sampled to see if they knew who the president of the university was. Of the 100 sampled, 17 knew who President Mantella was. 50 GVSU seniors were also sampled, and 35 stated they knew President Mantella.
Check conditions for both samples
n1&p-hat1:
17 >= 10
83 >= 10 ;
n2&p-hat2:
35 >= 10
50 >= 10
Define Ho and Ha
Documentary Horror Romance
Men 10 20 40
Women 35 15 30
Ho: Gender and preferred movie genre are independent / not related.
Ha: Gender and preferred movie genre are dependent / related.
Delta has 500 songs downloaded to her phone, and she wants to estimate what proportion of the songs are by a female artist. She takes an SRS of 50 songs on her phone and finds that 20 of the songs sampled are by a female artist. (95%)
Find the standard error. Round to the nearest ten-thousandth (fourth decimal place).
0.0693
What is a sample?
A subset of the population
100 GVSU freshman were sampled to see if they knew who the president of the university was. Of the 100 sampled, 17 knew who President Mantella was. 50 GVSU seniors were also sampled, and 35 stated they knew President Mantella.
What is p-hat1 and p-hat2?
p-hat1 = 17/100
p-hat2 = 35/50
What is the p-value for this matrix? Reject Ho?
Documentary Horror Romance
Men 10 20 40
Women 35 15 30
<0.001; reject Ho
Delta has 500 songs downloaded to her phone, and she wants to estimate what proportion of the songs are by a female artist. She takes an SRS of 50 songs on her phone and finds that 20 of the songs sampled are by a female artist. (95%)
What is the Margin of Error (MOE)?
Hint: Use SE that was NOT rounded.
0.1358
False positive
Type I Error
100 GVSU freshman were sampled to see if they knew who the president of the university was. Of the 100 sampled, 17 knew who President Mantella was. 50 GVSU seniors were also sampled, and 35 stated they knew President Mantella.
Find the margin of error
What is the dependent (response) variable? The independent (explanatory) variable?
Documentary Horror Romance
Men 10 20 40
Women 35 15 30
Dependent: Film genre
Independent: Gender
Delta has 500 songs downloaded to her phone, and she wants to estimate what proportion of the songs are by a female artist. She takes an SRS of 50 songs on her phone and finds that 20 of the songs sampled are by a female artist. (95%)
Find and interpret the confidence interval.
(0.2643, 0.5357)
We are 95% confident that the proportion of songs by female artists is between 26.43% and 53.57%.
False Negative
Type II Error
Fill in the blank for the confidence intervals:
(-,-) --> _________
(-,+) --> _________
(-,-) --> __________
(+,+) --> P1 is higher
(-,+) --> Both P1 and P2 are similar
(-,-) --> P2 is higher
What is the degrees freedom (df)?
Documentary Horror Romance
Men 10 20 40
Women 35 15 30
(3-1) * (2-1) = 2
Delta has 500 songs downloaded to her phone, and she wants to estimate what proportion of the songs are by a female artist. She takes an SRS of 50 songs on her phone and finds that 20 of the songs sampled are by a female artist. (95%).
Check the conditions!
20 >= 10
30 >= 10
When is the midterm?
October 7th (Next Friday)
100 GVSU freshman were sampled to see if they knew who the president of the university was. Of the 100 sampled, 17 knew who President Mantella was. 50 GVSU seniors were also sampled, and 35 stated they knew President Mantella.
Find the confidence interval (95%) and interpret the result
(-0.6768, -0.3832)
P2 is higher. GVSU seniors have a higher proportion of students who know President Mantella than GVSU freshman.