Chpt 9, 10 Flashcards
Confidence interval for an unknown parameter …
consists of an interval of numbers based on a point estimate.
The level of confidence represents
…the expected proportion of intervals that will contain the parameter if if a large number of samples is obtained.
Level of confidence is denoted (1 - alpha) * 100%
According to the Central Limit Theorem for Proportions, when you take samples from a population and compute a proportion from each one, you can consider the distribution of those proportions. This is called the sampling distribution for the population proportion.
The Central Limit Theorem tells us that the sampling distribution for the population proportion is approximately ____________ , with the true population proportion as its _______.
The Central Limit Theorem tells us that the sampling distribution for the population proportion is approximately NORMAL , with the true population proportion as its MEAN.
Formula:
stand dev of the sampling distribution is given by the formula
square root of (P(1-p)) / n
z-value
z-value = critical value of the distribution. The number of standard deviations the sample statistic can be from the parameter and still result in an interval that includes the parameter.
Ex: A 90% confidence interval for a parameter suggests that…
A 90% confidence interval for a parameter suggests that 90% of all possible samples will result in an interval that includes the unknown parameter and 10% of the samples will result in an interval that does not capture the parameter.
Increasing the level of confidence __________ the margin of error, resulting in a ______ confidence interval.
Increasing the level of confidence increases the margin of error, resulting in a wider confidence interval.
Increasing the confidence level will ___(incr/decr)______ the margin of error, since we will need to ___(incr/decr)______ the portion of the sampling distribution that we are selecting.
Increasing the confidence level will increase the margin of error, since we will need to increase the portion of the sampling distribution that we are selecting.
Conditions for estimating the value of a parameter
To use data to estimate the value of a parameter, the following 3 conditions must be met:
1) simple random sample
2) each sample size is no more than 5% of the population size
3) the Central Limit Theorem applies
Type I Error
Rejecting a true claim
a statement about a population parameter in the form of an equation or an inequality
Statistical claim
Type II Error
failed to reject a null hypothesis that is false.
a statistical claim in the form of a statement or an equation to be tested.
A statement of no change, no effect, or no difference. Status quo. Assumed to be true until evidence indicates otherwise.
null hypothesis
H0
a testable claim, often implied by a theory, that is either true or false.
An assumed proposition.
hypothesis
A statistical claim in the form of an inequality.
A statement we are trying to find evidence to support.
alternative hypothesis
H1
