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Inference for Categorical Data: Proportions - Coggle Diagram
Inference for Categorical Data: Proportions
Confidence Interval
Point Estimate
A statistic calculated from a sample such as a sample proportion or a sample mean
Confidence Interval
An interval estimate of the true parameter.
Equation
: statistic +- (critical value Z*)(standard error of statistic)
Interpretation
: We are ()% confident that the interval from () to () captures the true parameter of (context)
More Info
The width of an interval for a population proportion is proportional to 1/sq.root of n.
The width of a confidence interval tends to DECREASE with an INCREASE in sample size (n).
The width of a confidence interval increases as the confidence level increases.
The width of a confidence interval is exactly twice the margin of error.
Margin of error
Gives how much a value of a sample statistics is likely to vary from the value of the population parameter
ME will become smaller if we increase sample size or decrease our confidence level
Confidence Level
gives the percent of intervals, with repeated sampling of the same sample size, that will capture the true parameter
Interpretation
: if we take many samples of the same size from this population, about ()% of the results will capture the true proportion of (context).
Consructing CI
Standard error
The estimate for the standard deviation for the statistic
Equation
:
Critical Value
The boundaries that capture the middle C% of the standard normal distribution
Equation
: Inversenorm
Do a one sample z-interval for a population proportion if conditions are met
Random Sample/Radom Assignment
Independence(10% condition)
Normality (np, nq >= 10)
Interval Equation:
Use 4-step plan to solve the questions on confidence interval
Significance Test
Null Hypothesis
parameter = value
Alternative Hypothesis
parameter >, <, ≠ value
One-sided Hypothesis
A hypothesis test in which we believe that the alternative is either greater than or less than what is suggested in the null hypothesis (< or >)
Two-sided Hypothesis
A hypothesis test in which we believe the alternative is something different than the null hypothesis suggests (≠)
p-value
The probability that we would obtain a test statistics as extreme or more extreme if the null hypothesis is true
Interpretation:
If the true parameter of (context) is (p), the probability of getting a sample mean of (same sample size) is approximately (p-value)
If p-value > α: reject H0, have evidence for Ha
If p-value < α: fail to reject H0, no convincing evidence for Ha
Significance level (α)
Defuault α = 0.05
Usually given in question
Errors
Type 1: This is when the null hypothesis is rejected when it is in fact true
Type 2: This occurs when the null hypothesis is not rejected when it is false
Type 1 is usually a more serious error
Carrying out Signi. Tests
Do 1-sample z-test for a population proportion if conditions are met
: Randomness, Independence, Normality
Test statistic:
Then use normalcdf to find p-value
Compare p-value and α to see whether Ho is rejected or not
Diff in 2 pop. prop.
Significance test
Test Statistic:
Do 2-sample z test for the difference in 2 population proportions if conditions are met:
Randomness, Independence, Normality
Compare p-value and α to see whether Ho is rejected or not
Confidence Interval
CI Equation:
Do 2-sample z interval for the difference in two population proportions:
Randomness, Independence, Normality
