Chapter 8: Confidence Intervals

0.0(0)
studied byStudied by 8 people
learnLearn
examPractice Test
spaced repetitionSpaced Repetition
heart puzzleMatch
flashcardsFlashcards
Card Sorting

1/25

Study Analytics
Name
Mastery
Learn
Test
Matching
Spaced

No study sessions yet.

26 Terms

1
New cards
Confidence level
considered the probability that the calculated confidence interval estimate will contain the true population parameter.
2
New cards
Alpha level
is the probability that the interval does not contain the unknown population parameter.
3
New cards
standard error of the mean
𝜎 / √n
4
New cards
Confidence interval
an interval estimate for an unknown population parameter. This depends on
5
New cards
Confidence interval form
(point estimate – margin of error, point estimate + margin of error)
6
New cards
Empirical rule
Around 68% of values are within 1 standard deviation of the mean. Around 95% of values are within 2 standard deviations of the mean.
7
New cards
The margin of error
how many percentages points your results will differ from the real population value
8
New cards
Inferential statistics
We use sample data to make generalizations about an unknown population
9
New cards
Sample data
help us to make an estimate of a population parameter.
10
New cards
Point estimate
a single number computed from a sample and used to estimate a population parameter
11
New cards

is a point estimate for μ
12
New cards
p′
is a point estimate for ρ
13
New cards
s
is a point estimate for σ
14
New cards
Calculating the Error Bound
EBM \= (𝑧 𝛼/2)(𝜎/√n)
15
New cards
Confidence level interpretation
"We estimate with \___% confidence that the true population mean (include the context of the problem) is between \___ and \___ (include appropriate units)."
16
New cards
Increasing, wider
\_______ the confidence level increases the error bound, making the confidence interval \______.
17
New cards
Decreasing, narrower
\_______ the confidence level decreases the error bound, making the confidence interval \_______.
18
New cards
Sample size
Increasing the \_________ causes the error bound to decrease, making the confidence interval narrower.
19
New cards
Confidence interval
Decreasing the sample size causes the error bound to increase, making the \________ wider.
20
New cards
Student's t-distribution
a type of probability distribution that is similar to the normal distribution with its bell shape but has heavier tails
21
New cards
Standard deviation
a number that is equal to the square root of the variance and measures how far data values are from their mean; notation
22
New cards
Normal distribution
continuous random variable (RV) with pdf 𝑓(𝑥)\=(1 / 𝜎√2𝜋) 𝑒^–(𝑥–𝜇)^2/2𝜎^2, where μ is the mean of the distribution and σ is the standard deviation, notation
23
New cards
Degrees of freedom
the number of objects in a sample that is free to vary
24
New cards
df \= n - 1
the degrees of freedom for a Student’s t-distribution where n represents the size of the sample
25
New cards
The invT command requires two inputs
invT(area to the left, degrees of freedom) The output is the t-score that corresponds to the area we specified.
26
New cards
Z-score formula
If 𝑃′~𝑁(𝑝 , √𝑝𝑞/𝑛) then the z-score formula is 𝑧\=𝑝′−𝑝/√𝑝𝑞/𝑛