Distributions
What is the center in a population distribution?
Population parameter
Give the formula for calculating confidence Interval.
U = BPE + ME
There are 700 lakes in the state of Texas. If we take 70 of those lakes for our study, define the population and sample.
Population: 700 lakes in Texas.
Sample: 70 lakes in Texas
What is the difference between standard deviation and standard error?
SD is for sample and population.
SE is for Sampling distribution.
How does each dot in a sample and sampling distribution differ?
Each dot in a sample is a data value from the sample. Each dot in a sampling distribution is a sample statistics of the sample.
Find the confidence Interval for the following.
Sample statistic = 31
ME = 2
(29, 33)
We are trying to find the average size of all fishes in the lakes in Texas. We take 100 fishes from a lake in Texas. What is the sample and population? Is there any sampling bias?
Sample: 100 fishes in the lake
Population: All fishes in all lakes in Texas.
Yes, because we take fishes from only one lake.
How does SE change when the sample size is increased? What happens to the width?
SE decreases.
Width deceases.
Sample data = (29, 30, 31, 35, 36)
Population data = (27, 28, 29, 30, 31, 34, 35, 36, 37)
Sample average = 32.2.
The number 32.2 will be a dot in which distribution? Where will this distribution be centered?
Sampling distribution.
Center: 31.88
Find 95% CI for the following data.
Sample Statistic = 35
SE = 1
(33, 37)
We are trying to find the average size of all fishes in the lakes in Texas. We take 100 fishes from different lakes in Texas. What is the sample statistic and population parameter. Define them with proper notation.
Statistic: x̅ : average size of 100 fishes in the sample.
Parameter: μ : Average size of all the fishes in the lakes in Texas.
The CI of a distribution is (30, 40). When we change the sample size, the CI changes to (32, 37). Did we increase or decrease the sample size? How has the standard error changed?
We increased sample size.
SE decreased.
Sample data = (29, 30, 31, 35, 36)
Population data = (27, 28, 29, 30, 31, 34, 35, 36, 37)
Give one number that will be a dot in the sampling distribution. In sample distribution. In population distribution. Which distribution (if any) will have the number 31 in it?
32.2
Any from sample data.
Any from population data.
Both sample and population
Find and interpret the confidence Interval for the following question. Also define any parameters with proper notation.
We aim to find the mean number of hotdogs each by all people in the US per day. We take a sample of 10 people in the US and find that the average number of hotdogs each by people in the sample is 5.5. Given the standard error 1.3, find the 95% CI and interpret it.
μ = average number of hotdogs eaten by all people in the US per day.
(2.9, 8.1)
We are 95% confident that the average number of hotdogs eaten by all people in the US per day is between 2.9 and 8.1.
We take 30 students from a class in UT Tyler to estimate the proportion of females in the UT Tyler campus. We find that the proportion of females in the class is 0.43. What is our sample, population, population parameter and sample statistic? Give notations when applicable.
Sample: 30 students from the class.
Population: all students in UT Tyler campus
Parameter: p = proportion of all females in the campus of UT Tyler.
Statistic: (p-hat) = proportion of females in the class.
If the 95% CI is (42, 50), what is the BPE and SE?
BPE = 46.
SE = 2