1
If we use a 98% confidence interval instead of a 95% confidence interval, does the interval become narrow or wider?
The interval becomes wider because to have more confidence the interval becomes bigger so a 98% confidence interval would be wider than a 95% confidence interval.
What is Type 2 error
Type 2 error is an error that occurs when one fails to reject a null hypothesis that is actually false
As the alpha level increases what decreases? What increases?
The chance of type 2 error decreases
The chance of type 1 error increases
When using a one-sample t-test to construct a confidence interval for the mean of a finite population, a condition is that the population size be at least 10 times the sample size. The reason for the condition is to ensure that?
the degree of dependence among observations is negligible.
arrivals delayed=5.368+0.160(total operations)
r2=.842
Interpret the equation and the r2 value.
If there is zero total operations, the arrivals delayed is 5.368. For every total operation, there is 0.160 more arrivals delayed.
84.2% of the variability of the arrivals delayed is accounted for by the total operations.
Find a 95% confidence interval for the true approval rating of Joe Biden on May 4-6. We picked a random sample and got TIPP Insights to find our confidence interval.
TIPP Insights: 39% approval rating, 1,320 sample size
What is the test that we should use?
1 Proportion Z-Interval
We are comparing graduation rates and the percentage to college. Out of the 206 Massachusetts High Schools, we picked a random sample of 10 high schools.
Graduation rates: 98.3%, 78.5%, 90.6%, 84.6%, 84.3%, 86.2%, 97.2%, 94%, 86.7%, 70.4%
Percent to college: 61%, 83%, 89%, 82%, 49%, 83%, 63%, 92%, 100%, 82%
What test should we use?
2 Sample T-Test
We wanted to see if Joe Biden’s approval rate is less than 50% over his presidency. We used a simple random sample to find 10 polls that we could use in a list to find if Joe Biden's mean approval rating is less than 50%.
What type of test should we use?
1 Sample T-test
We wanted to see if the unemployment rate was lower in Winchester at 5.6% than the Massachusetts State average which is 7.7%.
What is the null and alternative hypothesis?
Null: Winchester has an equal unemployment rate to the state average
Alternative: Winchester has a lower unemployment rate then the state average
We wanted to see if the amount of money a movie had for a budget had a positive relationship with the audience score of the movie in 2007.
What test should we use to find out if there is a positive relationship between the 2?
linear regression t test
For a 1 Proportion Z Interval, what are the assumptions and conditions to proceed with the test?
10% Condition
Success/Failure Condition
Randomization Condition
Independence Condition
what are the assumptions and conditions for a 2 sample T test
Independence condition
Randomization condition
10% condition
Sucess/failure condition
What are the assumptions and conditions for a 1 sample T-test?
Nearly normal condition
Independence assumption
Randomization condition
10% condition
What are the assumptions and conditions for a 1 proportion z test?
10% Condition
Success/Failure Condition
Randomization Condition
Independence Condition
What are the assumptions and conditions for a LinRegTTest?
does the plot thicken
straight enough
Independence
Nearly Normal
Find a 95% confidence interval for the true approval rating of Joe Biden on May 4-6. We picked a random sample and got TIPP Insights to find our confidence interval.
TIPP Insights: 39% approval rating, 1,320 sample size
What is the interval and conclusion? (round to 3 decimal places)
(0.364, 0.416)
We are 95% confident that the true approval rating of Joe Biden is between 36.4% and 41.6%.
We wanted to compare the Massachusetts average SAT score for reading, writing, and math to Winchester's scores on the SAT to see if they were different from one another.
MA state avg: reading:492 writing:488 math: 507
Winchester avg: reading:583 writing:603 math: 617
What are the chi-square value, p-value, df, and conclusion? (round to 3 decimal places)
Chi-square=67.798
p=1.896x10^-15
df=2
There is sufficient statistical evidence to reject the null hypothesis meaning there is a difference in the test scores between the state avg and Winchester.
We wanted to compare the Massachusetts average SAT score for reading, writing, and math to Winchester's scores on the SAT were different.
What test should we use?
What are the null and alternative hypotheses?
Chi-square GOF test
Null: the Massachusetts average SAT score for reading, writing, and math to Winchester's scores on the SAT are the same
Alternative: the Massachusetts average SAT score for reading, writing, and math is different than Winchester's scores on the SAT
What are the assumptions and conditions for a chi-square GOF test?
counted data
independent groups
randomization
expected cell count
BONUS QUESTION WORTH DOUBLE 400x2=800
Swedish researchers investigated the relationship between chocolate consumption and stroke. The researchers gave a questionnaire about eating habits to a randomly selected sample of Swedish men. Based on the responses to the questionnaire, the men were classified into two groups. Group A consisted of the 9,250 men who ate the most chocolate per week, and group B consisted of the 9,250 men who ate the least chocolate per week. The researchers tracked the men's health for ten years. During that time, there were 458 cases of stroke among the men in group A and 543 cases of stroke among the men in group B.
Do the data provide convincing statistical evidence that Swedish men who would be classified into group A have a lower probability of stroke than Swedish men who would be classified into group B?
Please state hypothesis, type of test, assumptions and conditions, p-value, test statistic, and conclusion.
H0: pa = pb
HA: pa < pb
Type of test: 2-Proportion Z Test
Assumptions and conditions: Independence, Random, 10%, Success/Failure
p= 0.0029
t= -2.77
Because the p-value is very small, we reject the null hypothesis and conclude that the data provide statistical evidence that the Swedish men in group A have a lower probability of stroke than the Swedish men in group B
We wanted to see if there was a linear relationship between total operations and arrivals delayed at airports between 2003-2009 using a random sample of 10 airports.
Total operations: 154, 323, 62, 410, 60, 47, 147, 121, 371, 111
Delayed arrivals: 40, 41, 28, 85, 5, 9, 16, 48, 60, 10
What are the test statistic, p-value, df, equation, r^2 value, and conclusion? (round to 3 decimal places)
t=4.418
p=0.002
df=8
arrivals delayed=5.368+0.160(total operations)
r^2=.842
There is sufficient statistical evidence to reject the null hypothesis meaning there is a linear relationship between the total operations and arrivals delayed.
We are comparing graduation rates and the percentage to college. Out of the 206 Massachusetts High Schools, we picked a random sample of 10 high schools.
Graduation rates: 98.3%, 78.5%, 90.6%, 84.6%, 84.3%, 86.2%, 97.2%, 94%, 86.7%, 70.4%
Percent to college: 61%, 83%, 89%, 82%, 49%, 83%, 63%, 92%, 100%, 82%
What is the test statistic, p-value, and the conclusion we can reach with an alpha level of .15? (round to 3 decimal places)
p=0.148
t=1.531
df=13.857
We reject the null hypothesis because there is sufficient evidence to say the graduation rate of students and the percentage of students who go to college are different with an alpha level of .15.
We wanted to see if Joe Biden’s approval rate is less than 50% over his presidency. We used a simple random sample to find 10 polls that we could use in a list to find if Joe Biden's mean approval rating is less than 50%.
Approval ratings: 42%, 44%, 38%, 42%, 41%, 39%, 41%, 42%, 43%, 42%
What are the test statistic, p-value, and conclusion of the test? (round to three decimal places)
t=-15.309
p=4.723 x 10^-8
We reject the null hypothesis as there is sufficient statistical evidence that Joe Biden's approval rating is below 50%
We wanted to see if the unemployment rate was lower in Winchester than the Massachusetts State average which is 7.7%.
Winchester has a town population of 21171 and an unemployment rate of 5.6%.
What are the test statistic, p-value, and conclusion? (round to 3 decimal places)
z=-11.451
p=0
With a p-value of 0, there is sufficient evidence to reject the null hypothesis and conclude Winchester has a lower unemployment rate than the MA state average
We wanted to see if the amount of money a movie had for a budget had a positive relationship with the audience score of the movie in 2007.
What are the test statistic, p-value, equation, r^2, and conclusion?
Budget(in millions): 24, 20, 80, 30, 40, 85, 3.5, 3, 40, 10, 25, 13 ,140, 40, 60
Audience Score: 70, 44, 68, 56, 35, 64, 42, 62, 49, 47, 84, 59, 75, 50, 47
t=1.43
p=.088
r^2=13.6%
51.25+.136(Budget)=audience score
We fail to reject the null because there is insufficient statistical evidence to conclude there is a positive relationship between budget and audience score.