Confidence Intervals
When you increase the confidence level, what happens to the width of the interval?
the interval gets wider
What does the p-value represent?
The probability of getting evidence for Ha as strong or stronger than the observed when Ho is true.
How would one calculate the expected mean difference of a 2-prop z-interval
U=(P1-P2)
Justify that the independence assumption is correct?
N=200
Total Population= 1986
No, the sample size of 200, is greater than 198.6, which is 10% of the total population
A Maryland political poll is assessing public opinion for the upcoming election. They take a random sample of 500 registered voters and determine that 204 would reelect the incumbent candidate. A separate polling agency thinks that less people would reelect the incumbent and they decide to perform a Hypothesis Test to do so. What is the Null and Alternate Hypothesis?
Ho: p=204
Ha: p<204
For a 1-proportion z-interval, the middle value of the interval is equal to what?
The sample proportion
The probability of a type I error is equal to the ________?
Alpha level
What is the formula for performing a 2-proportion z interval?
statistic +/- critical value(standard error)
(x1-x2) +/- z-score (sqrt (P1 success)(P1 failures)/n1 + (P2 success)(P2 failures)/n2)
Justify the sample size assumption is met.
N=400
P(hat)=.63
Sample Size Assumption is met.
P(s)= (.63)(252) = 158.76 > 10
P(f) = (.37)(148) = 54.76 > 10
Claire is testing whether or not more than 45% of high school students have a summer job. What would a type 1 error in her test be?
A type 1 error would be rejecting that 45% of high school students have a summer job, when actually 45% of high school students do have a summer job.
What is the critical value for a 96% confidence interval?
2.054
If Ho: not guilty and Ha: guilty, state in context what a type II error would be.
Say not guilty but actually are guilty
What is the 4th assumption for 2-proportions?
Independent groups assumption
What bias indicates that this study is not randomized?
"A TV news station wants to get a sample of voters to garner create public opinion data. They decide to interview a sample of voters at a Trump rally and poll who they are voting for in the upcoming election"
Undercoverage Bias
John wants to determine how many of his students feel ready for their upcoming test. He believes that 45% of his students feel ready. He wants to determine from a sample of 100 students in his class if the true proportion is more or less than 45% of students. What type of inference test should he perform?
1-propz-test (hypothesis test)
A researcher wants to estimate the proportion of people in a city who support a new public transportation initiative. The researcher randomly surveys 400 residents of the city and finds that 260 of them support the initiative. Construct a 95% confidence interval for the true proportion of residents who support the initiative.
(0.6033,0.6967)
For a two-proportion z-test, how is an approximate population proportion calculated? (pooled data)
(x1+x2)/(n1+n2)
For a two-proportion z-test, how is an approximate population proportion calculated? (pooled data)
(x1+x2)/(n1+n2)
Marlene performs a hypothesis test and concludes that less than 83% of mall shoppers eat at the food court. What is the minimum size sample she could've polled from to meet the sample size assumption?
13 successes and 59 failures = 72 total people
Mark believes that more than 20% of the senior class take Multivariable Calculus. He wants to perform a hypothesis to test this belief. What would be the power of the test?
The power of the test would be rejecting that 20% of the senior class take multivariable calculus when more than 20% take multivariable calculus.
To test the effectiveness of a new teaching method, two groups of students are randomly assigned to either the new or old teaching method. After a semester, 45 of the 80 students of the new teaching method passed the final exam, and 30 of the 70 students of the old method passed the exam. Construct a 95% confidence interval for the difference in proportions between the two methods.
(-0.0253,0.2931)
As the difference between Ho and Ha increases, power _______ and beta ______.
Power increases, beta decreases.
A school administrator wants to compare the proportion of students passing a standardized test in two different schools. In School A, 150 out of 200 students passed the test.In School B, 130 out of 180 students passed the test. Construct a 95% confidence interval for the difference in the proportions of students passing the test between School A and School B.
(−0.0610,0.0886)
A television ad for pharmaceuticals airs containing a phone number in which viewers call in to voice whether or not they are interested in the product. Of a sample of 20 callers, 15 said they supported the new product. Which assumptions are not met in this study?
Randomization and Sample Size assumption
Justin is worried that his kids are eating too much ice cream. He calculates that in the month of June, his kids went out for ice cream 16 of the 30 days. However, his kids also eat ice cream at home and he calculated that they had ice cream at home 22 of the 30 days. Justin wants to perform a hypothesis test to examine the difference in proportions between ice cream eaten out and at home. What would a type 2 error in his test be?
A type 2 error would be failing to reject that there is no difference between ice cream eaten out and ice cream eaten at home when there actually is a statical difference between the two proportions.