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40 Cards in this Set
- Front
- Back
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For a normal distribution, a critical value is:
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a z score on the borderline separating the z scores that are likely to occur from those that are unlikely to occur.
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The expression z(sub ɑ) denotes:
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the z score with an area of ɑ to its right.
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What is the best point estimate of the population proportion?
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the sample proportion p̂
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The sample proportion is used to estimate the true value of the population proportion through the construction of:
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a confidence interval
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Is an appropriate sample size necessary to estimate a population proportion?
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yes
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population proportion is denoted by:
sample proportion is denoted by: |
population proportion is denoted by: p
sample proportion is denoted by: p̂ |
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If we want to estimate a population proportion with a single value, the best estimate is:
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the sample proportion p̂
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The sample proportion p̂ is called a point estimate because:
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it consists of a single value
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A point estimate is:
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a single value (or point) used to approximate a population parameter.
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The best point estimate of the population proportion (p) is:
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the sample proportion (p̂)
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A confidence interval or interval estimate, is:
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a range or interval of values used to estimate the true value of a population parameter, sometimes abbreviated as CI.
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A confidence interval is associated with:
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a confidence level
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The confidence level gives us:
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the success rate of the procedure used to construct the confidence interval.
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The confidence interval is often expressed as the:
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probability or area 1 - ɑ, where alpha is the complement of the confidence level.
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The confidence level is the:
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probability 1 - ɑ that the confidence interval actually does contain the population parameter.
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The confidence level is also called the:
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degree of confidence or the confidence coefficient.
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ɑ is the:
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complement of the confidence level.
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The most common choices for the confidence level are:
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90%, 95%, and 99%.
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The margin of error is denoted by:
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E
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The margin of error is aka:
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the maximum error of the estimate
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The margin of error is found by:
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multiplying the critical value and the standard deviation of sample proportions.
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The stdv of the sample proportion formula is:
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√{p̂q̂/n}
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The margin of error formula is:
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z* • √{p̂q̂/n}
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What are the requirements for using a confidence interval to estimate a population proportion?
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1) The sample is a simple random sample
2) Conditions for binomial distribution or met. 3) np ≥ 5 and nq ≥ 5. |
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What is the formula for the Confidence Interval?
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P̂ − E < p < p̂ + E
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What is the procedure for constructing a confidence interval for p?
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1) Verify the requirements are met.
2) Find the critical value z* 3) Evaluate the margin of error. 4) Use the confidence interval formula. |
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How do we determine the sample size in order to estimate the population proportion p?
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we solve for n in the margin of error formula
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How do we determine the sample size in order to estimate the population proportion p if p̂ is not known?
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we substitute the value 0.5 for both p̂ and q̂
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The formula for finding n =
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(z*/ E)² •p̂•q̂
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z(sub ɑ)/2 can be denoted by:
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z*
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p̂ =
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x/n
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What is the rounding rule when calculating z*?
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3 digits after the decimal point.
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What is the rounding rule when calculating n?
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Always round n up to the next integer.
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What is the procedure for using the TI-84 to calculate the confidence interval?
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stat, tests, 1-propzint..., enter x value, n value, C-level, then press enter.
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If we only know the confidence interval limits, we can find the:
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sample proportion and margin of error
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What is the formula for finding the sample proportion from the confidence interval limits?
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p̂ = (upper C.I. limit) + (lower C.I. limit) / 2
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What is the formula for finding the margin of error from the confidence interval limits?
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E = (upper C.I. limit) − (lower C.I. limit) / 2
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The formula for standard error is:
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√{p̂q̂ / n}
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Interpret the C.I. of 99%:
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There is a 99% confidence that the true population proportion (p) is between (state the lower confidence interval and the upper confidence interval).
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What does 99% confidence mean?
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About 99% of all possible random samples of given size
n = (state what n is) will produce confidence intervals that contain the true population proportion. |
