Bio Stat (exam 2) lecture 12 & 13

margin of error

tells us how far our sample estimate might reasonably be from the true population parameter

• smaller MOE = more precise estimate

• larger MOE = less precise estimate

confidence level

tells us how confident we are in the method to create our confidence interval

higher confidence level

wider interval

lower confidence level

narrower interval

confidence interval

range of values that is likely to include a population parameter with a certain degree of confidence

example confidence interval

A 95% confidence interval for the population mean is (50, 60)

• we are 95% confident that the true population mean falls between 50 and 60

statistical hypotheses

a claim about a population parameter that we want to investigate

null hypothesis

assumes there is no change

alternative hypothesis

Represents the claim that we are trying to find evidence for (3 kinds)

• two-sided (does not equal )

• right-sided ( u > 50)

• left-sided ( u < 50)

p value

The probability of obtaining a result as extreme as, or more extreme than, the observed result, assuming the null hypothesis is true

• tells us how surprising our sample result would be if the null hypothesis were actually true

small p value

strong evidence against H0

large p value

not enough evidence against H0

conclusion of statistical hypothesis test

• a mathematical way to use data to assess the plausibility of a hypothesis

• When completing a hypothesis test, we compare the p-value to the significance level (a)

• There are two possible conclusions

when p value < or equal to a

reject H0

ex.

• p-value: 0.03

• a = 0.05

• We reject!

when p value > a

fail to reject H0

ex.

• p value : 0.08

• a = 0.05

• we fail to reject H0

impact of a (significance level)

The significance level (α) is the cutoff we use to determine whether we have enough evidence to reject the null hypothesis

increasing a makes it

easier to reject H0

decreasing a makes it

harder to reject H0

type 1 error

happens when we reject the null hypothesis even though it is actually true

z test & t tests

tests used to make inferences about a population mean

z test

• Population standard deviation is known

• uses the standard normal (Z) distribution

• uses population standard deviation in calculations

t test

• Population standard deviation is unknown

• uses the t -distribution

• Uses the sample standard deviation

test statsitcs

measures how compatible a sample estimate is with the null hypothesis