stats chapter 7
confidence interval (Cl)
- is a range (or an interval) of values used to estimate the true value of a population parameter. aka interval estimate - probability 1 − α
If the confidence level is 99%, what is the value of alpha?
0.01
90% critical value
1.645
95% critical value
1.96
Find the critical value z Subscript alpha divided by 2 that corresponds to 95%
1.96
99% critical value
2.575
sample proportion
<p is the best point estimate of the population proportion p.
A magazine provided results from a poll of 1500 adults who were asked to identify their favorite pie. Among the 1500 respondents, 12% chose chocolate pie, and the margin of error was given as plus or minus5 percentage points. Given specific sample data, which confidence interval is wider: the 95% confidence interval or the 80% confidence interval? Why is it wider?
A 95% confidence interval must be wider than an 80% confidence interval in order to be more confident that it captures the true value of the population proportion.
Which of the following is NOT an observation about critical values?
A critical value is the area in the right-tail region of the standard normal curve.
The value of Modifying Above <q with caret is
found from 1- <p
margin of error
likely difference (with probability 1 - α, such as 0.95) between the observed proportion the and the true value of the population proportion <p
A _______ is a single value used to approximate a population parameter.
point estimate
The value of p is
population proportion
z x/2
s a critical value that is a z-score that separates an area of x/2 in the right tail of the standard normal distribution
critical value
s a z-score on the borderline separating sample statistics that are unlikely to occur (or significantly high or low) from those that are likely to occur(or not significant)
The value of E is
the margin of error
The value of ModifyingAbove <p with caret is
the sample proportion
The value of n is
the sample size
99% (or 0.99) confidence level:
α = 0.01
95% (or 0.95) confidence level:
α = 0.05
90% (or 0.90) confidence level:
α = 0.10
Which of the following groups has terms that can be used interchangeably with the others?
Percentage, Probability, and Proportion
A newspaper provided a "snapshot" illustrating poll results from 1910 professionals who interview job applicants. The illustration showed that 26% of them said the biggest interview turnoff is that the applicant did not make an effort to learn about the job or the company. The margin of error was given as plus or minus 3 percentage points. What important feature of the poll was omitted?
The confidence level
A magazine provided results from a poll of 1000 adults who were asked to identify their favorite pie. Among the 1000 respondents, 13% chose chocolate pie, and the margin of error was given as plus or minus5 percentage points. Describe what is meant by the statement that "the margin of error was given as plus or minus5 percentage points."
The statement indicates that the interval 13%plus or minus5% is likely to contain the true population percentage of people that prefer chocolate pie.
Which of the following is NOT a requirement for constructing a confidence interval for estimating the population proportion?
The trials are done without replacement.
We must be careful to interpret confidence intervals correctly. There is a correct interpretation and many different and creative incorrect interpretations of the confidence interval 0.405 < p < 0.455
We are 95% confident that the interval from 0.405 to 0.455 actually does contain the true value of the population proportion p
We can use a sample proportion to
a confidence interval to estimate the true value of a population proportion, and we should know how to interpret such confidence intervals.