Statistics 1 - Chapter 07

Point Estimate

A single value (or point) used to approximate a population parameter.

SE Mean

Standard Error of the Mean

Critical Value

The number on the borderline separating sample statistics that are likely to occur from those that are unlikely to occur.
This is commonly denoted as z(sub)?/2. It is a z score with the property that it separates an area of ?/2 in the right tail of the st

Confidence Level

The probability 1-? that the confidence interval actually does contain the population parameter.
Also called the: Degree of Confidence or Confidence Coefficient.
Ex: 1-? = 90%. We are 90% confident that the confidence interval contains the population para

Confidence Interval

A range or interval of values used to estimate the true value of a population parameter. Sometimes abbreviated as CI.

p

Population proportion that possesses a specific characteristic

p?

Sample proportion that possesses a specific characteristic
Obtained by adding the upper & lower confidence interval limit and dividing by 2.

q hat

Sample proportion that does not possess a specific characteristic
1 - p?

E

Margin of Error.
Maximum likely difference between the observed sample proportion p? and the true value of the population proportion p.
Found by multiplying critical value & standard deviation of the sample proportions.

Degrees of Freedom

Usually n-1. There will be times when it is not n-1 (later chapters)
Number of sample values that can vary after certain restrictions have been imposed on all data values.
Abbreviated as df

Z Distribution

A normally distributed set of specially scaled values whose mean is always equal to zero and area under curve must equal 1.

student t distribution

Bell-shaped probability distribution that is symmetrical about its mean.
The sampling distribution of the T statistic.
Picture shows the t statistic formula.

Chi-Square Distribution

Used to develop estimates of variances & standard deviations.
They have no negative values (because everything is squared).

Critical Values are based off of?

1) Under certain conditions, the sampling distribution of sample proportions can be approximated by a normal distribution.
2) A z score associated with a sample proportion has a probability of ?/2 of falling in the right tail.
3) The z score separating th

Confidence Interval for Population Variance

Requirements:
1) Sample is a simple random sample
2) Population must have normally distributed values even if sample is large.

Confidence Interval for Population Standard Deviation

Requirements:
1) Sample is a random sample
2) Population must be normally distributed (doesn't matter if sample size is large)

Confidence Interval for Estimating a Population Proportion p

Requirements:
1) The sample is a simple random sample
2) Conditions for the binomial distribution are satisfied
3) There are at least 5 successes and 5 failures.

Confidence Interval for Estimating a Population Mean with ? not known

Requirements:
1) Sample is a simple random sample
2) Either the sample is from a normally distributed population or n > 30

Confidence Interval for Estimating a Population Mean with ? known

Requirements:
1) The sample is a simple random sample
2) The value of the population standard deviation ? is known.
3) Either or both of these is satisfied: The population is normally distributed or n > 30

Formula to find the Sample Size Required to Estimate a Population Mean

Requirements:
1) The sample must be a simple random sample.

Formula to find the Sample Size to Estimate a Population Proportion

Requirements:
The sample must be a simple random sample of independent subjects.

Below is for reference only

Below is for reference only

Round-Off Rule for Confidence Interval Estimates of p

Round the confidence interval limits for p to three significant digits.

Round-Off Rule for Determining Sample Size

If the computed sample size n is not a whole number, round the value of n up to the next larger number.

Round-Off for Confidence Intervals Used to Estimate ?

1) When using the original set of data to construct a confidence interval, round the confidence interval limits to one more decimal place than is used for the original set of data.
2) When the original set of data is unknown and the only summary statistic

Finite Population Correction Factor

When sampling w/o replacement and the sample size n is greater than 5% of the finite population size N, adjust the standard deviation of sample means ?(sub)x-bar by multiplying it by the finite population correction factor.