module 5 sampling distribution

Sampling distribution of the sample proportion is when ___ is unknown

P

Step one of proportion

mu p hat= p

Step two of proportion

standard deviation p hat = square root p(1-p)/n

Step three of proportion

CLT

• np >/= 10 (number of success)

• n1-p) > 10 (number of failures)

~ p hat ~ normal

Sampling distribution of the sample mean is when ____ is unknown

mu

Step one of mean

mu y bar = mu

Step two of mean

Standard deviation year bar = standard deviation/ squared root n

Step 3 of mean

y ~ normal → y bar ~ normal

Or

y is not normal → clt y bar ~ normal

N>/= 30 only use if y is not normal.

Step 1 of total

mu total = n mu

Step 2 of total

standard deviation total = square root n standard deviation.

Step 3 of total

y ~ normal → total. ~ normal

Or

y ~ normal → clt total ~ normal

n >/= 30

y bar total formula

Total/n

→ total = n(y bar)

Total formula

y1 + y2 + y3 …. yn

Population parameter

numerical measure such as the mean, median, mode, range, variance, or standard deviation calculated for a population data; and is written with Greek letters. Eg. µ and σ.

• usually unknown and constant

Sample statistic

summary measure calculated for a sample data set; it is written with Latin letters. Eg. 𝒚 bar, s

• observed after sample is selected

• Regarded as random before sample is selected

Sampling variability

The value of the statistic varies from sample to sample.

Sampling distribution

The distribution of all the values of a statistic.

Population proportion

Is obtained by taking the ratio of the number of successes in a population to the total number of elements in the population.

sampling distribution model

for how a sample proportion varies from sample to sample allows us to quantify that variation and how likely it is that we’d observe a sample proportion in any particular interval.

Independence assumption

The sampled values must be independent of each other.

Sample size assumption

The sample size must be sufficiently large.

Randomization condition

The data values must be sampled randomly.

Large enough sample condition

The CLT doesn’t tell us how large a sample we need. For now, you need to think about your sample size in the context of what you know about the population.

Central Limit Theorem (CLT)

The fundamental theorem of statistics.

• works better (and faster) the closer the population model is to a Normal itself. It also works better for larger samples.