Point EstimatesPoint Estimates
A point estimatepoint estimate is a single number determined from a sample that is used to estimate the corresponding population parameter.
Confidence IntervalsConfidence Intervals
Confidence IntervalConfidence Interval Developed from a sample. Provides a range of likely values for a parameter.Expresses the confidence level that the true population parameter is included.
Confidence IntervalsConfidence Intervals
Point EstimateLower Confidence
LimitUpper Confidence
Limit
95% Confidence Intervals95% Confidence Intervals(Figure 7-3)(Figure 7-3)
0.95
z.025= -1.96 z.025= 1.96
Confidence IntervalConfidence Interval- General Format -- General Format -
Point Estimate (Critical Value)(Standard Error)
Confidence IntervalsConfidence Intervals
The confidence levelconfidence level refers to a percentage greater than 50 and less than 100. For a given size sample it is the percentage that the interval will contain the true population value.
Confidence Interval Confidence Interval EstimatesEstimates
CONFIDENCE INTERVAL CONFIDENCE INTERVAL ESTIMATE FOR ESTIMATE FOR ( ( KNOWN) KNOWN)
where:z = Critical value from
standard normal table
= Population standard deviation
n = Sample size
nzx
Example of a Confidence Example of a Confidence Interval Estimate for Interval Estimate for
A sample of 100 cans, from a population with = 0.20, produced a sample mean equal to 12.09. A 95% confidence interval would be:
039.009.1210020.096.109.12
n
zx
12.051 ounces
12.129 ounces
Margin of ErrorMargin of Error
The margin of errormargin of error is the largest possible sampling error at the specified level of confidence.
Margin of ErrorMargin of ErrorMARGIN OF ERROR (ESTIMATE FOR MARGIN OF ERROR (ESTIMATE FOR
WITH WITH KNOWN) KNOWN)
where:e = Margin of errorz = Critical value = Standard error of the
sampling distributionn
nze
Example of Impact of Example of Impact of Sample Size on Sample Size on
Confidence IntervalsConfidence IntervalsIf instead of sample of 100 cans, suppose a sample of 400 cans, from a population with = 0.20, produced a sample mean equal to 12.09. A 95% confidence interval would be:
0196.009.1240020.096.109.12
n
zx
12.051 ounces
12.129 ounces
12.0704 ounces
12.1096 ouncesn=400
n=100
Student’s t-DistributionStudent’s t-Distribution
The t-distributiont-distribution is a family of distributions:Bell-shaped and symmetric Greater area in the tails than the normal.Defined by its degrees of freedom. The t-distribution approaches the normal distribution as the degrees of freedom increase.
Confidence Interval Confidence Interval EstimatesEstimates
CONFIDENCE INTERVAL CONFIDENCE INTERVAL (( UNKNOWN) UNKNOWN)
where:t = Critical value from t-
distribution with n-1 degrees of freedom
= Sample means = Sample standard deviationn = Sample size
nstx
x
Confidence Interval Confidence Interval EstimatesEstimates
CONFIDENCE INTERVAL-LARGE CONFIDENCE INTERVAL-LARGE SAMPLE WITH SAMPLE WITH UNKNOWN UNKNOWN
where:z =Value from the standard
normal distribution = Sample means = Sample standard deviationn = Sample size
nszx
x
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