Formulas
n-1
What is the formula to find degrees of freedom?
State, Plan, Do, Interpret
What is the Four Step Process?
We are __% confident that the interval from A to B captures the true _________.
What is an interpretation of a confidence interval?
90%= 1.645
95%= 1.960
99%= 2.576
What are the Z-score critical values?
The table used to find a t-score?
What is table B?
SD over the square root of n
What is the formula for the standard deviation of the sampling distribution?
Random, 10%, Central Limit Theorem
What are the conditions for constructing a confidence intreval?
If we make many ___% confidence levels we expect about __% to capture the true mean.
What is an interpretation of a confidence level?
Latoya wants to estimate the proportion of the seniors at her boarding school who like the cafeteria food. She interviews an SRS of 50 of the 175 seniors and finds that 14 think the cafeteria food is good. Which of the conditions for calculating a confidence interval for the population proportion đť‘ť has not been met?
What is the 10% condition?
The calculator command to find a t-score
What is Inverse t?
Point estimate plus or minus margin of error
What is the general formula for any confidence interval?
On table B and is used for means.
What is a t score?
A New York Times/CBS News Poll asked a random sample of U.S. adults the question “Do you favor an amendment to the Constitution that would permit organized prayer in public schools?” Based on this poll, the 95% confidence interval for the population proportion who favor such an amendment is (0.63, 0.69).What is the point estimate that was used to construct this interval? What is the margin of error?
What is 𝑝̂ =0.66 and M.O.E. = 0.03?
According to a recent Pew Research Center report, many American adults have made money by selling something online. In a random sample of 4579 American adults, 914 reported that they earned money by selling something online in the previous year. The 98% confidence interval resulting from this survey is 0.1996±0.01370.1996±0.0137. Interpret the confidence interval.
What is we are 98% confident that the interval from 0.1859 to 0.2133 captures đť‘ť the true proportion of American adults who have earned money by selling something online in the previous year?
Types of data
What is categorical or quantitative?
Z score times SD over the square root of n
What is the formula to find margin of error?
A statistic that provides a reasonable guess about the population parameter
What is a point estimate?
People love living in California for many reasons, but traffic isn’t one of them. Based on a random sample of 572 employed California adults, a 90% confidence interval for the average travel time to work for all employed California adults is 23 minutes to 26 minutes. Describe how nonresponse might lead to bias in this survey.
What is People who have longer travel times to work might have less time to respond to a survey. This would cause our estimate from the sample to be less than the true mean travel time to work?
According to a recent Pew Research Center report, many American adults have made money by selling something online. In a random sample of 4579 American adults, 914 reported that they earned money by selling something online in the previous year. Calculate and interpret the standard error for these data.
What is about 0.0059?
Allows us to generalize about a population
What is a simple random sample?
Sx over the square root of n
What is the formula to find standard error of the mean?
Increases with confidence level and decreases when the sample size increases. Also in never accounts for bias.
What is the margin of error?
A particular type of diet cola advertises that each can contains 12 ounces of the beverage. Each hour, a supervisor selects 10 cans at random, measures their contents, and computes a 95% confidence interval for the true mean volume. For one particular hour, the 95% confidence interval is 11.97 ounces to 12.05 ounces. Does the confidence interval provide convincing evidence that the true mean volume is 12 ounces?
What is No?
According to a recent Pew Research Center report, many American adults have made money by selling something online. In a random sample of 4579 American adults, 914 reported that they earned money by selling something online in the previous year. Assume the conditions for inference are met. Construct a 98% confidence interval for the proportion of all American adults who would report having earned money by selling something online in the previous year.
What is (0.1859, 0.2133)?
A surprising number of young adults (ages 19 to 25) still live in their parents’ homes. The National Institutes of Health surveyed independent random samples of 2253 men and 2629 women in this age group. The survey found that 986 of the men and 923 of the women lived with their parents. Let 𝑝1 the true proportion of young men who live in their parents’ homes and 𝑝2 the true proportion of young women live in their parents’ homes. We are 99% confident that the interval from 0.051 to 0.123 captures 𝑝1–𝑝2 the true difference in the proportions of young men and young women who live in their parents’ homes. Does this interval give convincing evidence of a difference between the population proportions?
What is yes?