Stats Exam 2

Sample standard deviation

s

Calculate standard error of sample mean

s/sqrt n

When to use z test (sample mean distribution )

If population standard deviation is known for sample means and for all proportion distributions

E (margin of error) = z* stdev / sqrt n

When to use t test (sample mean distribution)

If the population standard deviation sigma is unknown

E (margin of error) = t * stdev / sqrtn

degrees of freedom

n-1

T Interval requirements

1. Simple random sample

2. Independent; without replacement, sample size should be less than 5% of population

3. Population is normal or CLT should apply (30+)

Calculate Sample Size for Sample Mean Distribution

n = (z*stdev / E)²

Planning stdev can come from reported SD prior studies, observations and calculating it yourself, or doing range/4

Calculate Sample Size for Proportion Distribution

n = (z² *p*q / E²) E is a percentage here not a whole number

if you dont know p and q use 0.25

Standard Error for Proportions

S=sqrt (pq/n)

Margin of Error for Proportions

z * sqrt (pq/n)

Requirements for Wald Interval (Proportion)

1. Simple random sample

2. Binomial requirements

3. 5 successes and 5 failures

Requirements for Binomial Distribution

1. independent trials

2. fixed number of trials

3. only 2 outcomes

4. the possibility of success is the same in each trial

Probability of Exactly x

[ n ! / (n-x)!x! ] p^x q^n-x

n=number of trials

x= number of successes

p=prob of success

q=prob of failure

standard deviation of binomial

sqrt npq

Range Rule of Thumb

lower than mean - 2stdev is significantly low, higher than mean + 2stdev is significantly high

0.05 probability rule

if the probability is less or equal to 0.05 it is significantly high/low (x=successes)

Requirements for Poisson Distribution

1. random events

2. independent

3. uniformly distributed (same rate of event across interval)

STdev of Poisson

sqrt mean

Rule for Approximating Binomial Using Poisson

n >= 100 and np <= 10. if satisfied, mean = np

Calculating z score from one raw x value

(x - mean / population stdev)

Converting z score to variable x/raw value

x=mean + z*stdev

Calculating z score of mean of x value (x hat)

(x - mean) / (population stdev/sqrt n)