Download Ch8-10 Vocabulary2 (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
Hypothesis (p. 478) – a statement regarding a characteristic of one or more populations.
Hypothesis testing (p. 478) – a procedure, based on sample evidence and probability, used to test
statements regarding a characteristic of one or more populations.
Steps in Hypothesis Testing (p. 478) –
1.
Make a statement regarding the nature of the population.
2.
Collect evidence (sample data) to test the statement.
3.
Analyze the data to assess the plausibility of the statement.
Null hypothesis, H0 (p. 478) – a statement to be tested. The null hypothesis is a statement of no
change, no effect, or no difference and is assumed true until evidence indicates otherwise. (always
contains a statement of equality)
Alternative hypothesis, H1 (p. 478) – a statement that we are trying to find evidence to support.
Four Outcomes from Hypothesis Testing (p. 479) –
Level of significance, α (p. 481) – The probability of making a Type I error.
[That is P(rejecting H0 given that H0 is true) = α.]
Sec 10.2: Hypothesis Tests for a Population Proportion
Statistically significant (p. 485) – When observed results are unlikely under the assumption that the
null hypothesis is true, we say the result is statistically significant and we reject the null hypothesis.
Hypothesis Testing Using the Classical Approach (p. 486) – If the sample proportion is too many
standard deviations from the proportion stated in the null hypothesis, we reject the null hypothesis.
P-value (p. 487) – the probability of observing a sample statistic as extreme or more extreme than the
one observed under the assumption that the statement in the null hypothesis is true. Put another
way, the P-value is the likelihood or probability that a sample will result in a statistic such as the one
obtained if the null hypothesis is true.
Hypothesis Testing Using the P-Value Approach (p. 487) – If the probability of getting a sample
proportion as extreme or more extreme than the one obtained is small under the assumption the
statement in the null hypothesis is true, reject the null hypothesis.
5 STEPS FOR HYPOTHESIS TESTING (about a population proportion) ( p. 487-488) –
Sec 10.3: Hypothesis Tests for a Population Mean
5 STEPS FOR HYPOTHESIS TESTING (about a population mean) (p. 497-498) –
Practical significance (p. 501) – refers to the idea that, while small differences between the statistic
and parameter stated in the null hypothesis are statistically significant, the difference may not be large
enough to cause concern or be considered important.
[Large sample sizes can lead to results that are statistically significant, while the difference between
the statistic and parameter in the null hypothesis is not enough to be considered practically
significant.]