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21 Cards in this Set
- Front
- Back
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Standard error of the sample means: |
V(xbar) = v/radical(n) S(xbar) = s/radical(n) (when v is unknown) |
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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 |
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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 |
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Confidence Interval of population mean: |
Xbar - E =< M =< xbar + E P - E =< Pi =< P + E |
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The best estimate of the population mean is: |
The sample mean; also called point estimate |
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To construct a CI: |
1. Calculate Z by using CL 2. Calculate Vxbar 3. Calculate E 4. Find the CI using M |
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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) |
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When population SD is unknown: |
We use sample SD instead: V ===> S |
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Difference between normal distribution and t-distribution: |
- Normal distribution is bell-shaped - t-distribution is mound shaped |
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Degree of freedom: |
df = n - 1 |
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As n increases more than 30: |
t approaches Z |
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To find t: |
1. Calculate df 2. Use CL by using the t-table |
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Population distribution is normal, sampling distribution of the sample mean is: |
Normal |
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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 |
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1. P: 2. Pi: |
1. Sample proportion 2. Population proportion 3. Binomial distribution |
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Sample size (n) to estimate a population mean for Z only: |
n = (Z. V/E)^2 |
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3 factors to determine sample size for population mean: |
1. Margin of error (E) 2. Confidence level (to find Z) 3. Standard deviation (V) |
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Sample size (n) to estimate a population proportion (P =~ Pi): |
n = P(1 - P)(Z/E)^2 n = Pi(1 - Pi)(Z/E)^2 |
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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) |
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The calculated sample size (n) should always be rounded . . . |
To the next whole number (up) |
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No estimate of n: |
P = 0.5 |
