The probability that a confidence interval procedure produces an interval missing the true population value is written with the Greek letter alpha.
Missing Word
alpha
Alpha is the chance of a miss, and it equals 1 minus the confidence level. For a 95% confidence level, alpha is 0.05.
Category: Interpreting Confidence Intervals
Question 2
The t-distribution was developed by William Gosset, a brewery chemist who published under a pen name.
Missing Word
Gosset
William Gosset studied small samples while working at the Guinness brewery in Dublin and published as Student, which is why the distribution is called Student's t.
Category: Student's t-Distribution
Question 3
Like the standard z curve, every t-distribution has its line of symmetry at zero.
Missing Word
symmetry
A line of symmetry splits a distribution into two mirror-image halves. The t-distribution shares this property with the standard z curve, centered at zero, but has more area in its tails.
Category: Student's t-Distribution
Question 4
Compared with the standard z curve, a t-distribution has more area in its tails, so its critical values are larger for the same confidence level.
Missing Word
tails
The tails are the far ends of a distribution. Because s varies from sample to sample, the t-distribution spreads more probability into its tails than the standard z curve does, which pushes t critical values above the matching z values; the difference shrinks as the degrees of freedom grow.
Category: Student's t-Distribution
Question 5
The population standard deviation is written with the Greek letter sigma, while the sample standard deviation is written s.
Missing Word
sigma
Sigma describes the spread of the whole population. When it is known, a confidence interval for mu uses the z-distribution.
Category: Error Bound
Question 6
Before computing p', the plus-four method adds 2 imaginary observations of each kind to the sample.
Missing Word
2
The plus-four method adds two successes and two failures, so x becomes x + 2 and n becomes n + 4. The adjustment makes proportion intervals more accurate for small samples.
Category: Plus-Four Method
Question 7
In proportion problems, the outcome being counted is called a success even when it is unwanted, such as finding a defective part.
Missing Word
success
In proportion problems a success is simply the outcome being counted, whether or not it is desirable. The sample proportion p' is the number of successes divided by n.
Category: Population Proportion
Question 8
In proportion problems, a sampled individual who does not have the trait being counted is recorded as a failure.
Missing Word
failure
A failure is any outcome other than the one being counted. The estimated proportion of these is q' = 1 - p'.
Category: Population Proportion
Question 9
The quantity q' = 1 - p' is the complement of the sample proportion p'.
Missing Word
complement
The complement of an event is everything outside it, so its probability is 1 minus the event's probability. Together p' and q' add to 1.
Category: Population Proportion
Question 10
Using sample data to draw conclusions about a population, as a confidence interval does, is called statistical inference.
Missing Word
inference
Inference is reasoning from a sample to a population. Confidence intervals are one form of inference, estimating a parameter with a range of plausible values.
Category: Point Estimates
Question 11
The number of yes answers among n independent trials, each with the same chance p, follows a binomial distribution.
Missing Word
binomial
A binomial distribution counts successes in a fixed number of independent trials. When n is large, the sample proportion x / n is approximately normal, which justifies the z interval for p.
Category: Population Proportion
Question 12
For a small sample, a t-interval assumes the data come from a population that is approximately normal.
Missing Word
normal
The t procedures are built on the assumption of a normal or nearly normal population. With small samples, strong skewness or outliers can make the interval unreliable.
Category: Student's t-Distribution
Question 13
A confidence interval gives a range of plausible values for a population parameter, such as a population mean or proportion.
Missing Word
parameter
A parameter is a fixed but usually unknown number that describes a population. Confidence intervals estimate parameters using statistics computed from a sample.
Category: Point Estimates
Question 14
A t-interval from a small sample can be badly distorted by outliers, values that lie far from the rest of the data, because they pull both x-bar and s.
Missing Word
outliers
Outliers are data values unusually far from the rest. Both the sample mean and the sample standard deviation are sensitive to them, so with a small sample a single outlier can shift the center of a t-interval and change its width a great deal.
Category: Student's t-Distribution
Question 15
Because a sample must contain a whole number of people, the result of the sample size formula is rounded up to the next integer.
Missing Word
rounded
Sample sizes are rounded up, never down, because a smaller sample would give an error bound slightly larger than the target.
Category: Width and Sample Size