Confidence Intervals Flashcards
The average amount you spend on a lunch during the week is not known. Based on past experience, you are willing to assume that the standard deviation is $1.75. If you take a random sample of 25 lunches, what is the value of the standard deviation of xbar?
Answer: $0.35
Reasoning: 1.75/sqrt(25)= $0.35
In the setting of the previous two Check-in questions, about 95% of all samples will capture the true mean in the interval xbar plus or minus
$______
. Fill in the blank.
Answer: $0.70
Reasoning: 95% = 2 standard deviations, $0.35*2 = $0.70
A level C _______ for a parameter is an interval computed from sample data by a method that has probability C of producing an interval containing the true value of the parameter.
confidence interval
How does increasing sample size change the margin of error?
It reduces the margin of error
Any confidence interval has two parts: _______ and _______.
an interval computed from the data, a confidence level.
The _______ states the probability that the method will give a correct answer. That is, if you use 95% confidence intervals, in the long run 95% of your intervals will contain the true parameter value.
confidence level
Determining sample size. Refer to the previous exercise. You really want to use a sample size such that about 95% of the averages fall within ± 5 minutes of the population mean μ.
B. Using the standard deviation you calculated in part (A), determine the number of students you need to sample in order to achieve this.
*SD = 0.04167
n=1607
An announced poll result was 56.3% ± 1%. Can we be certain that the true population percent falls in this interval? Explain your answer.
Results are based on telephone interviews. . . with a random sample of 160,498 adults, living in all 50 U.S. states and the District of Columbia. For results based on the total sample of national adults, the margin of sampling error is plus or minus 1 percentage points at the 95% confidence level.13
No, we can only be 95% sure.
