Vocab
This can be found by dividing the sample standard deviation by the square root of the sample size, and then multiplying by t.
Margin of Error
What parameter MUST be present in order for me to use a Z-confidence interval for means?
Population standard deviation or sigma
Which two do I need to find Margin of Error: sample mean, critical value, population size, confidence level
critical value and population size
If (99.8, 104.6) is a 90% confidence interval for a sample of fifteen basketball scores, what is your conclusion about the average scores of the population?
We are 90% confident that the interval contains the population mean basketball scores.
In a survey of 1035 US adults, 745 say they want to play pickleball regularly. What is p-hat and q-hat?
.72 and .28
Which of these changes when I use a t-distribution as opposed to a Z-distribution: Sample size, confidence level, or critical value?
critical value
If the mean of a sample is 2.3 and the margin of error is 1.5, what is the confidence interval?
(.8,3.8)
If a confidence interval is from 26.32 to 35.85, what is the mean of the sample?
31.085
If my sample size is 12, how many degrees of freedom are there?
11
This is built around a sample statistic in an effort to better approximate a population parameter.
Confidence Interval
Should I use a t-distribution or a z-distribution or neither? The data is skewed right. Suppose that you want to find out the average weight of all players on the football team at a particular College. You are able to select ten players at random and weigh them. The mean weight of the sample of players is 198 lbs, with a standard deviation of 11.50 lbs.
Neither
Find the Margin of Error for a 95% z-confidence interval with a standard deviation of 24.2 and a sample size of 40.
7.5
The average heights of a random sample of 400 people from a city is 1.75 m. It is known that the heights of the population are random variables that follow a normal distribution with a standard deviation of 0.4 m. Determine the interval of 95% confidence for the average heights of the population.
n = 400 x = 1.75 σ = 0.4 c = 0.95 z* = 1.96 (1.75 ± 1.96 • 0.4/20 ) → (1.7108, 1.7892)
In a survey of 2022 US adults, 1167 think antibiotics are effective against viral infections. Find a 95% confidence interval for the population proportion.
(.556, .599)
This is added and subtracted from the sample mean in order to construct a confidence interval
Margin of Error
Should I use a t-distribution or Z or neither? The average heights of a random sample of 400 people from a city is 1.75 m. It is known that the heights of the population are random variables that follow a normal distribution with a standard deviation of 0.4 m. Determine the interval of 95% confidence for the average heights of the population.
Z
What is the margin of error for a sample with a critical value of 1.76, a sample size of 64, and a sample standard deviation of 3.5?
0.77
Suppose that you want to find out the average weight of all players on the football team at a particular College. You are able to select ten players at random and weigh them. The mean weight of the sample of players is 198 lbs, with a standard deviation of 11.50 lbs. Construct a 90 percent confidence interval for the population weight, if you presume the players' weights are normally distributed.
(192, 204)
When do you use a t-interval instead of z? Tell me all qualifications
Sample size less than 30
Normally distributed
No population SD
You randomly select 18 adult male atheletes and measure the resting heart rate of each. The sample mean heart rate is 64 beats per minute with a sample standard deviation of 2.5 beats per minute. Assuming the heart rates are normally distributed, should you use the z distribution, t-distribution or neither to construct a confidence interval?
t-interval
If the margin of error of a sample is 3.45, the sample size is 16, and the critical value for the confidence level is 1.876, then what is sample standard deviation?
7.356
If a sample of 36, has a mean of 29, and a standard deviation of 4.3, find a 90% confidence interval for the population mean.
(28.055,29.945)
If Mrs. Beigel was not a teacher, what would be her profession?