Math 146 final exam (SCC) questions and answers

Random variable for the average of a sample

X-bar

Random variable for a sample proportion

P-hat

Random variable for a population

X

4 conditions of P-hat

1. random sample

2. independence between values in sample

3. n/N < 10%

4. np >or= 10, nq >or= 10

4 conditions of X-bar

1. random sample

2. independence between values in sample

3. n/N < 10%

4. Central limit theorem holds

Central limit theorem guidelines

Symetric unimodal - n >or= 3 required

Slightly skewed - n >or= 15 required

Very skewed - n >or= 30 required

Equation for 95% CI

*all letters have a "hat" to indicate sample population

Explain Confidence Intervals (CI)

Given a sample from a population, the CI indicates a range in which the population mean is believed to be found, indicating the lower and upper boundaries.

2 ways to narrow a confidence interval

1. increase sample population (n)

2. decrease confidence level

p vs. P-hat vs. p-value

p: population proportion

P-hat: sample population proportion

p-value: area of the tail of a distribution

4 conditions for hypothesis testing

Same conditions as P-hat

1. random sample

2. independence between values in sample

3. n/N < 10%

4. np >or= 10, nq >or= 10

Interpreting p-value vs. alpha

p-value > alpha : reject the null

p-value < alpha : fail to reject the null

What is alpha?

Alpha is the area under the curve where a null hypothesis would be rejected

Type 1 error

rejected null when null was actually true

Type 2 error

failed to reject null when null was actually false

Error vs. CI

Error is 1/2 of the width of a confidence interval

Null hypothesis

the status quo, involves an equality (=), may be called "baseline"

Alternative hypothesis

not the status quo, what is suspected to be really happening

Probability of a type 1 error

P(type 1 error) = alpha

How the results of a CI test and hypothesis test can be consistent

If a 2-tailed hypothesis test is done with alpha=1-(confidence level) then the results will be consistent

4 conditions for hypothesis testing involving X-bar

similar to 4 conditions of X-bar

1. random sample

2. independence between samples

3. n/N < 10%

4. Central limit theorem holds

As n grows, a T-distribution will...

become a normal distribution

Positive association/correlation in a scatter plot

as x increases, y also increases

Negative association/corrolation

as x increases, y decreases

Describe the coefficient for association/correlation

represented with r

is between -1 and 1

can only be used for linearly associated data

Equation for line of best fit

y-hat = ax+b

a= slope

b= y-intercept

Explanatory variable

the x-variable

Response variable

the y-variable