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Constructing a Confidence Interval
Checking Conditions
Is the sample random? ( so we can generalize ) Is the sample less than 10% of population ( so we can do the standard deviation formula ) Does it meet the Large Counts Condition ( is it normal or not ? ) ( so we can use normal calculations ) np >= 10 and n(1-p) >= 10
Critical Value — Number of standard deviations from Mean to achieve a given % confidence similar to z score so we call it z
90% of data fall within 1.64 standard deviations of the mean → z^* = 1.64 95% of data fall within 1.96 - > z^* = 1.96 99% of data fall within 2.58 → z^* = 2.58
To find any critical value, invNorm( % they give you , 0, 1)
Formula for Confidence Interval
Confidence interval = point estimate +- margin of error = point estimate +- critical value * standard error = p +- z *
margin of error = critical value * standard error
p(1-p) n