Descriptors of normal distribution of random variables
- Graph centered around the mean
- Graph of distribution is symmetric
- Graph of distribution is bell-shaped
Which groups can be used interchangeably when working with normal distributions?
- Area
- Probability
- Percentages
- Relative Frequencies
A continuous random variable has a __________ distribution of its values are spread evenly over the range of possibilities.
Uniform
Requirements of density curve
- Total area under curve must be 1
- Every point on the curve must have a vertical height that is 0 or greater
- Curve cannot fall below horizontal axis
Standard normal distribution
- Area under curve must equal 1
- Mean is 0 and standard deviation is 1
- Graph is symmetric
Finding probabilities associated with distributions that are standard normal distributions is equivalent to _________.
Finding the area of the shaded region representing that probability
The _________ tells us that for a population with any distribution, the distribution of the sample means approaches a normal distribution as the sample size increase.
Central limit theorem
What conditions produce a negative z-score?
Value left of the mean
If you are being asked to find the 85th percentile, you are being asked to find ___________.
A data value associated with an area of 0.85 to its left
What does the notation z (a) indicate?
Denotes the z score with an area of a to it’s right
The __________ states that if, under a given assumption, the probability of a particular observed event is exceptionally small, we conclude that the assumption is probably not correct.
Rare event rule for inferential statistics
A critical value. z(a), denotes the _______.
Z-score with an area of a to its right
Population proportion concepts
- Using sample statistic to estimate population proportion is using inferential statistics.
- Sample proportion is best point estimate of population proportion.
- We can use a sample proportion to construct a confidence interval to estimate the true value of a population proportion.
- Knowing the sample size necessary to estimate a population proportion is important.
Which of the following groups has terms that can be used interchangeably with the others?
Percentage, probability, and proportion
A ___________ is a single value used to approximate a population parameter.
Point estimate
Confidence interval
Gives range of values to estimate population parameter rather than a single value.
What is needed to determine minimum sample size to estimate population proportion?
- Margin of error
- a
- Z a/2
Confidence interval for estimating a population proportion p: Notation
p= population proportion
^p= sample proportion
n= number of sample values (sample size)
E= margin of error
Za/2= critical value
^q= found from evaluating 1-^p
Confidence interval requirements
- Sample is a simple random sample
- Conditions for the binomial distribution are satisfied.
- There are at least 5 successes and at least 5 failures
Properties of student t distribution
- Same general shape & symmetry as the standard normal distribution with more variability expected with small samples
- Mean of t=0
- Standard deviation > 1
- Student t distribution is different for different sample sizes
The ________ is the best point estimate of the population mean.
Sample mean
Derived from confidence level
- Point estimate of mean
- Margin of error
- Difference between the limits
Requirements for constructing confidence interval to estimate mean with sigma unknown
- Sample is simple random sample
- Sample measures quantitative value
- Either population is normally distributed or n> 30, or both
The __________ distribution is used to develop confidence interval estimates of variances or standard deviations.
Chi square
