Definitions &
Equations
Equations
When finding a critical value for a two-tailed confidence interval, why do we divide the significance level (alpha) by 2?
To split the total area outside the confidence interval equally between the two tails of the distribution.
Find the critical t-value for a 95% confidence interval with a sample size of 16.
2.131
Find the margin of error for a population proportion with a z-score of 1.96, a proportion of 50%, and a sample size of 100.
0.098
A sample mean is 1.32, the critical value is 1.96, and the margin of error is 0.0335. Construct a confidence interval for the mean.
(1.2865, 1.3535)
Which distribution do you use to construct a confidence interval for a population proportion?
z-distribution
How do we find a Confidence Interval?
point estimate ± MOE
What is the critical z-value for a population proportion with a 90% confidence level?
1.645
Find the margin of error for a 95% confidence interval with a sample size of 25 and a sample standard deviation of 6.
2.477
The General Social Survey asked 1972 adults how many years of education they had. A sample mean is 13.37, with a standard deviation of 3.13. The critical t value is 2.327. Construct a 98% confidence interval.
(13.206, 13.534)
The population standard deviation is unknown, and you are constructing a confidence interval for a population mean. Which distribution do you use?
t-distribution
Before constructing a confidence interval, we must check that these assumptions are met...
1. Simple Random Sample
2. The sample size is large (n > 30), or the population is approximately normal.
A researcher wants to construct a 99% confidence interval for a population mean. The population standard deviation is known. Find the critical value.
2.576
For a study on public wi-fi, usage times are recorded over a period of 50 randomly selected days. The average daily usage time is found to be 2.5 hours. Assume the population standard deviation is 0.9 hours. Calculate the margin of error for a 90% confidence interval.
0.21
In a sample of 42 water specimens taken from a construction site, 26 contained detectable levels of lead. Construct a 90% confidence interval for the proportion of water specimens that contain detectable levels of lead.
(0.4957, 0.7423)
You are constructing a confidence interval for a population mean, and the population standard deviation is known. Which distribution do you use?
z-distribution
If a population is less than 30, what's one way we check to see if it is normal?
Create a box plot
Find the critical t-value for a 99% confidence interval with a sample size of 20 when the population standard deviation is unknown.
2.861
In a sample of 36 smart home devices of a certain brand, the mean number of potential vulnerabilities per device was 7.8, with a standard deviation of 2.1. Find the margin of error for a 95% confidence interval.
0.7105
A college admissions officer takes a simple random sample of 100 entering freshmen and computes their mean mathematics SAT score to be 458. Assume the population standard deviation is 116. Construct a 99% confidence interval for the mean mathematics SAT score for the entering freshman class.
(428, 488)
Which distribution do you use to construct a confidence interval for a population standard deviation?
Chi-square distribution
How do we find the MOE for a population proportion?
MOE = z-score * SQRT [ (p * (1 - p)) / n ]
Find the lower and upper chi-square critical values for a 95% confidence interval with a sample size of 20. (HINT: use CHISQ.INV in Excel)
Lower: 8.907
Upper: 32.852
A gym surveys 500 of its members to determine the proportion interested in high-intensity training classes. Out of the surveyed members, 325 express interest. For a 90% confidence interval, find the margin of error.
0.0351
A sociologist sampled 200 people who work in computer-related jobs and found that 42 of them have changed jobs in the past six months. Construct a 95% confidence interval for the proportion of those who work in computer-related jobs who have changed jobs in the past six months.
(0.154, 0.267)
You want to estimate the percentage of college students who play a sport using sample data. Which type of confidence interval do you use?
Confidence Interval for a population proportion