Vocabulary
This term represents the middle value in a data set when it is ordered
Median
This is the most commonly used confidence interval in college statistics
95%
The formula for calculating the margin of error for a population mean is
E=Zc σ/√n
If a 95% confidence interval for the mean height of a population is (64, 68), this is what we conclude
We are 95% confident the true population mean is between 64 and 68
In a survey of 200 students, you find that 60% are in favor of a new campus policy. What is the 95% confidence interval for the true proportion?
(0.54,0.66)
This is the symbol used for the sample mean
x̄
A confidence interval increases in width when this factor increases
Sample Size
You want to estimate the mean height of adult men. A sample mean of 50 men gives a sample mean of 68 inches and a standard deviation of 3 inches. What is the margin of error for a 95% confidence interval?
0.832
What is the meaning of 99% confidence interval for the population proportion?
We are 99% confident that the true population proportion lies within the interval
You measure the heights of 50 students and calculate a 95% confidence interval for the mean height of 150 cm ± 4. What does this mean?
The true population mean height is between 146cm and 154cm
This type of error occurs when a null hypothesis is rejected when it is actually true
Type 1 error
This is the critical value for a 99% confidence interval using the standard normal distribution
2.576
Given a sample proportion of 0.6 and a sample size of 100, calculate the standard error for a confidence interval
0.049
You calculate the 95% confidence interval and find it is (10,20). What is the interpretation?
There is a 95% chance that the true population parameter is between 10 and 20
A researcher wants to estimate the average income of a population of workers. She collects a sample of 100 workers and finds the sample mean income is $35k with a standard deviation of $5k. What is the 95% confidence interval for the average income?
($34,000-$36,000)
This is a range of values, derived from a sample, that is used to estimate the true population parameter
Confidence Interval
This factor determines how precise the estimate from a sample will be
Margin of error
Find the 95% confidence interval for a sample mean of 100, with a standard deviation of 15 and a sample size of 25
(95.4, 104.6)
A confidence interval for a mean difference in a paired t-test is (-4.5, 2.5). What does this suggest?
No significant difference as 0 falls in the interval
Given a sample size of 200 and a sample proportion of 0.75, calculate the standard error for the population proportion.
0.033
This is the probability of observing a sample statistic as extreme or more extreme than the one observed, assuming the null hypothesis is true
P-value
If a confidence interval is wider, this is likely to happen to the level of confidence
Increase
If the sample size doubles, this is what happens to the standard error
Decreases by a factor of √2
What does a narrow confidence interval suggest about the precision of the estimate?
Suggests a more precise estimate of the population parameter
A biologist is studying the weight of fish in a river. He collects a sample of 25 fish and calculates a 99% confidence interval for the mean weight. What effect would increasing the sample size have on the confidence interval?
It would make the confidence interval narrower