Symbols and Their Meanings
When dealing with sampling distributions, the letter n represents this.
What is the sample size?
According to the Central Limit theorem, we can assume a sampling distribution will be normal if n is at least 30 OR if this condition is met.
The population distribution is normal.
Given a sampling distribution of the difference of sample proportions from different populations, the mean of the sampling distribution is calculated by this.
What is p1 - p2 or the difference of the proportions?
This is the name used to describe the shape of a normal distribution.
What is the bell-curve? (or symmetric AND unimodal)
A certain statistic a is being used to estimate a population parameter A. The expected value of a is larger than A. Statistic a is exhibiting this property.
What is a is biased?
When talking about a population parameter, the letter p represents this.
What is the population proportion?
These conditions need to be met for a sampling distribution of a sample proportion to be approximately normal.
What is np greater than 10 and n(1-p) greater than 10?
In a certain region of the country, the proportion of the population with blue eyes is currently 34 percent. A random sample of 84 people will be selected from the population. This is the mean of the sampling distribution of the sample proportion of people with blue eyes for samples of size 84.
What is 0.34?
Given a normal distribution, this percentage of the data will be contained within 2 standard deviations of the mean.
What is 95%?
What is by a factor of 16?
When talking about a statistic for the sampling distribution, this Greek letter represents the mean.
What is mu
Given a sampling distribution of a sample mean where the population distribution is uniform, this is how we determine if the sampling distribution will be normal.
What is n is at least 30?
Given a sampling distribution of a sample mean, this is how we calculate the standard deviation of the sampling distribution.
What is sigma/sqrt(n)?
Given a normal distribution with mean 50 and standard deviation of 5, this represents the middle 68 percent of the data.
What is 45 to 55?
The distribution of the number of siblings for students at a large high school is skewed to the right with mean 2.4 siblings and standard deviation 1.1 sibling. A random sample of 25 students from the high school will be selected, and the mean number of siblings in the sample will be calculated. This best describes the shape and standard deviation of the sampling distribution.
What is approximately normal and SD < 1.1 (= 1.1/5 or 0.22)?
When talking about a statistic for the sampling distribution, this Greek letter represents the standard deviation.
What is sigma?
At a national convention attended by many educators, about 25 percent of the attendees are from the northeast. Of all the attendees of the national convention, 25 will be selected at random to receive a free book. These are the mean and standard deviation of the sampling distribution of the proportion of attendees from the northeast for samples of size 100
Mean = .25, standard deviation = 0.0433
Given a normal distribution with mean 50 and standard deviation 5, this is the probability of randomly selecting a value below 43.
What is 0.081? (or 8.1%)
A survey of 75 randomly selected dentists in the state of Virginia results in 64% who would recommend the use of a certain toothpaste. The population proportion is known to be p = 0.67. For samples of size 75, this is the best interpretation of the mean of the sampling distribution.
The mean of sample proportions from all random samples of size 75 from dentists in Virginia is 0.67.
This is the symbol that is used when talking about variance.
What is sigma squared?
Given that a population has a proportion of 0.9, this is the minimum sample size for a sampling distribution to be approximately normal.
What is 100?
The mean age of the employees at a large corporation is 37.5 years, and the standard deviation is 6 years. A random sample of 16 employees will be selected. These are the mean and standard deviation of the sampling distribution of the sample mean for samples of size 16
What is mean = 37.5 and SD = 6/4 (or 1.5)?
Given a normal distribution with mean 67 and standard deviation 6.7, this value would represent the 67th percentile?
What is 69.95?
Given a sampling distribution of the difference of sample means, this is the interpretation of the standard deviation of the sampling distribution being s=2.5
The mean of a randomly selected sample from this population will typically vary from the mean by about 2.5