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21 Cards in this Set

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Standard error of the sample means:

V(xbar) = v/radical(n)


S(xbar) = s/radical(n) (when v is unknown)

Maximum or margin error of estimate:

1. E = Z.V (xbar)


2. E = t.S (xbar) (when v is unknown)


3. E = Z.radical (P(1 - P)/n) for proportion

To calculate Z:

1. Divide the comfidence level (CL) by 2:


2. Find the nearest value in the body of the Z-table


3. Go and find the Z-value

Confidence Interval of population mean:

Xbar - E =< M =< xbar + E


P - E =< Pi =< P + E

The best estimate of the population mean is:

The sample mean; also called point estimate

To construct a CI:

1. Calculate Z by using CL


2. Calculate Vxbar


3. Calculate E


4. Find the CI using M

Interpret the CI:

1. The limit of the CI of the population mean are (xbar - E) & (xbar + E)


2. We expect that certain% of similarly comstructed CI to contain population mean (or population proportion when P is used)

When population SD is unknown:

We use sample SD instead:


V ===> S

Difference between normal distribution and t-distribution:

- Normal distribution is bell-shaped


- t-distribution is mound shaped

Degree of freedom:

df = n - 1

As n increases more than 30:

t approaches Z

To find t:

1. Calculate df


2. Use CL by using the t-table

Population distribution is normal, sampling distribution of the sample mean is:

Normal

Population distribution is unknown, the sampling distribution of the sample mean is:

1. n >= 30: guaranteed as normal by CLT


2. n < 30: assume population distribution is normal ===> sampling distribution will be normal

1. P:


2. Pi:

1. Sample proportion


2. Population proportion


3. Binomial distribution

Sample size (n) to estimate a population mean for Z only:

n = (Z. V/E)^2

3 factors to determine sample size for population mean:

1. Margin of error (E)


2. Confidence level (to find Z)


3. Standard deviation (V)

Sample size (n) to estimate a population proportion (P =~ Pi):

n = P(1 - P)(Z/E)^2


n = Pi(1 - Pi)(Z/E)^2

3 factors to determine the sample size for population proportion:

1. Margin error (E)


2. Confidence level (to find Z)


3. Proportion or SD for proportion:


Vp = P (1 - P)

The calculated sample size (n) should always be rounded . . .

To the next whole number (up)

No estimate of n:

P = 0.5