Download Ch8-10 Vocabulary (with definitions)

MTH243 – Probability and Statistics – T. Davenport
Ch8 – Vocabulary
Sec 8.1: Distribution of the Sample Mean
Sampling distribution (p. 401) – a probability distribution for all possible values of the statistic
computed from a sample of size n.
̅ (p. 401) – the probability distribution of all possible
Sampling distribution of the sample mean 𝒙
values of the random variable 𝑥̅ computed from a sample of size n from a population with mean 𝜇 and
standard deviation 𝜎.
[We will err on the side of caution and say that, if the distribution of the population is unknown or not
normal, then the distribution of the sample mean is approximately normal provided that the sample
size is greater than or equal to 30.]
Sec 8.2: Distribution of the Sample Proportion
𝑥
̂ (p. 414) – given by 𝑝̂ = where x is the number of individuals in the sample with
Sample proportion, 𝒑
𝑛
the specified characteristic. 𝑝̂ is a statistic that estimates the population proportion, p.
MTH243 – Probability and Statistics – T. Davenport
Ch9 – Vocabulary
Sec 9.1: Estimating a Population Proportion
Point estimate (p. 426) – the value of a statistic that estimates the value of a parameter.
Confidence interval (p. 427) – an interval of numbers based on a point estimate for an unknown
parameter. [Point estimate ± margin of error]
Margin of error (p. 428) – determines the width of the confidence interval.
Level of confidence (p. 427) – the expected proportion of intervals that will contain the parameter if a
large number of different samples is obtained. The level of confidence is denoted (1 − 𝛼) ∙ 100%.
A 95% level of confidence means that 95% of all possible samples result in confidence intervals that
include the parameter (and 5% of all possible samples result in confidence intervals that do not
include the parameter). A 95% level of confidence does not tell us there is a 95% probability the
parameter lies between the lower and upper bound.
Critical value (p. 430) – the value 𝑧𝛼 represents the number of standard deviations the sample statistic
2
can be from the parameter and still result in an interval that includes the parameter.
(1-α)•100% Confidence Interval (p. 432) –
Margin of error, E (p. 433) – in a (1 − 𝛼) ∙ 100% confidence interval for a population proportion is
given by
𝐸 = 𝑧𝛼 ∙ √
2
𝑝̂(1−𝑝̂)
𝑛
Sample size needed (p. 435) –
Sec 9.2: Estimating a Population Mean
Student’s t-distribution (p. 441) – if the population from which the simple random sample of size n is
drawn follows a normal distribution, the distribution of 𝑡 =
𝑥̅ −𝜇
𝑠
√𝑛
follows Student’s t-distribution with
n-1 degrees of freedom, where 𝑥̅ is the sample mean and s is the sample standard deviation.
(1-α)•100% Confidence Interval (p. 444) –
Margin of error, E (p. 446) – in a (1 − 𝛼) ∙ 100% confidence interval for a population mean is given by
𝑠
𝐸 = 𝑡𝛼 ∙
√𝑛
2
Sample size needed (p. 447) –
MTH243 – Probability and Statistics – T. Davenport
Ch10 – Vocabulary
Sec 10.1: The Language of Hypothesis Testing
Uniform probability distribution (p. 361) – a distribution in which any two intervals of equal length are
equally likely.
Sec 10.2: Hypothesis Tests for a Population Proportion
Sec 10.3: Hypothesis Tests for a Population Mean