Stats 250 exam 1

parameter

deals with total population

statistic

deals with sample

M

the mean of parameter

μ̂

the mean of the statistic

σ

the standard deviation of the parameter

σ̂

the standard deviation of the statistic

pi

the proportion of the parameter

pi-hat

the proportion of the statistic

What summaries do quantitative data use?

mean, standard deviation, IQR

What summary does categorical data use?

proportion

What does z-test statistic measure?

how many null standard deviations our observed sample proportion pi is from the hypothesized null population proportion

What is the definition of a p-value?

how compatible data observed from a random sample are with the hypothesized value of the population parameter. The smaller the p-value, the less compatible with null hypothesis

what lower tail is this for? <

TRUE

what lower tail is this for? >

FALSE

normal distribution

unimodal and symmetric

what skew of graph is this?

left skewed

what skew of graph is this?

right skewed

What value is the center?

pi

variability increase

sample size decreases

variability decreases

sample size increases

sample distribution

everything selected in one random sample, meant to vary

sampling distribution

all of the samples themselves, not specifically selected, meant to show a pattern

population distribution

shows all of the set of values

p-value= less than 0.01

very strong evidence against the null hypothesis and in support of the alternative hypothesis

p-value= 0.01-0.05

strong evidence against the null hypothesis and in support of the alternative hypothesis

p-value= 0.05-0.1

some evidence against the null hypothesis and in support of alternative hypothesis

p-value= above 0.1

not enough evidence against the null hypothesis and in support of the alternative hypothesis

Total area under a normal curve

1

How large must be the sample size be to use CLT?

n=25

t-test

how many null standard deviations our observed sample proportion pi is from the hypothesized null population proportion, used for quantitative data

degrees of freedom

n-1

What does the CLT state?

as sample size increases, the distribution of the sample mean approaches a normal distribution, regardless of the population's underlying distribution

If sample size increases, what happens to p-value?

p-value decreases