Ch. 8 Interval Estimation

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Essentials of Modern Business Statistics 7e Essentials ofModern BusinessStatistics 7e Anderson Sweeney Williams Camm Cochran.
2018 Cengage Learning 2018 Cengage Learning May not be scanned copied or duplicated or posted to a publicly accessible website in whole or in part except for use as permitted in a license distributed with a certain product or service orotherwise on a password protected website or school approved learning management system for classroom use Essentials of Modern Business Statistics 7e Interval Estimation.
Population Mean s Known Population Mean s Unknown Determining the Sample Size Population Proportion Big data and Interval estimation.
2018 Cengage Learning May not be scanned copied or duplicated or posted to a publicly accessible website in whole or in part except for use as permitted in a license distributed with a certain product or service orotherwise on a password protected website or school approved learning management system for classroom use Essentials of Modern Business Statistics 7e Margin of Error and the Interval Estimate A point estimator cannot be expected to provide the exact value of.
the population parameter An interval estimate can be computed by adding and subtracting amargin of error to the point estimate Point Estimate Margin of Error The purpose of an interval estimate is to provide information about.
how close the point estimate is to the value of the parameter 2018 Cengage Learning May not be scanned copied or duplicated or posted to a publicly accessible website in whole or in part except for use as permitted in a license distributed with a certain product or service orotherwise on a password protected website or school approved learning management system for classroom use Essentials of Modern Business Statistics 7e Margin of Error and the Interval Estimate.
The general form of an interval estimate of a population mean is Margin of Error 2018 Cengage Learning May not be scanned copied or duplicated or posted to a publicly accessible website in whole or in part except for use as permitted in a license distributed with a certain product or service orotherwise on a password protected website or school approved learning management system for classroom use Essentials of Modern Business Statistics 7e .
Interval Estimate of a Population Mean s Known In order to develop an interval estimate of a population mean the margin of error must be computed using either the population standard deviation s or the sample standard deviation s.
s is rarely known exactly but often a good estimate can beobtained based on historical data or other information We refer to such cases as the s known case 2018 Cengage Learning May not be scanned copied or duplicated or posted to a publicly accessible website in whole or in part except for use as permitted in a license distributed with a certain product or service orotherwise on a password protected website or school approved learning management system for classroom use .
Essentials of Modern Business Statistics 7e Interval Estimate of a PopulationMean s KnownThere is a 1 probability that the value of a samplemean will provide a margin of error of or less .
2 2 2018 Cengage Learning May not be scanned copied or duplicated or posted to a publicly accessible website in whole or in part except for use as permitted in a license distributed with a certain product or service orotherwise on a password protected website or school approved learning management system for classroom use Essentials of Modern Business Statistics 7e Interval Estimate of a Population.
Mean s Known 2018 Cengage Learning May not be scanned copied or duplicated or posted to a publicly accessible website in whole or in part except for use as permitted in a license distributed with a certain product or service orotherwise on a password protected website or school approved learning management system for classroom use Essentials of Modern Business Statistics 7e Interval Estimate of a Population Mean s Known.
Interval Estimate of mwhere is the sample mean1 is the confidence coefficientz 2 is the z value providing an area of 2 in the uppertail of the standard normal probability distribution.
s is the population standard deviationn is the sample size 2018 Cengage Learning May not be scanned copied or duplicated or posted to a publicly accessible website in whole or in part except for use as permitted in a license distributed with a certain product or service orotherwise on a password protected website or school approved learning management system for classroom use Essentials of Modern Business Statistics 7e .
Interval Estimate of a Population Mean s KnownValues of za 2 for the Most Commonly Used Confidence LevelsConfidence a a 2 Look up Area za 290 1 05 9500 1 64595 05 025 9750 1 960.
99 01 005 9950 2 576 2018 Cengage Learning May not be scanned copied or duplicated or posted to a publicly accessible website in whole or in part except for use as permitted in a license distributed with a certain product or service orotherwise on a password protected website or school approved learning management system for classroom use Essentials of Modern Business Statistics 7e Meaning of Confidence.
Because 90 of all the intervals constructed using will contain thepopulation mean we say we are 90 confident that the interval includes the population mean m We say that this interval has been established at the 90 confidence level .
The value 90 is referred to as the confidence coefficient 2018 Cengage Learning May not be scanned copied or duplicated or posted to a publicly accessible website in whole or in part except for use as permitted in a license distributed with a certain product or service orotherwise on a password protected website or school approved learning management system for classroom use Essentials of Modern Business Statistics 7e Interval Estimate of a Population Mean Known.
Example Lloyds Department storeEach week Lloyds department store selects a simple random sample of100 customers in order to learn about the amount spent per shoppingtrip The historical data indicates that the population follows a normaldistribution .
During most recent week Lloyd s surveyed 100 customers n 100 and obtained a sample mean of 82 Based on historical data Lloyd snow assumes a known value of 20 The confidence coefficient to beused in the interval estimate is 95 2018 Cengage Learning May not be scanned copied or duplicated or posted to a publicly accessible website in whole or in part except for use as permitted in a license distributed with a certain product or service or.
otherwise on a password protected website or school approved learning management system for classroom use Essentials of Modern Business Statistics 7e Interval Estimate of a PopulationMean KnownExample Lloyds Department store.
95 of the sample means that can be observed are within 1 96 ofthe population mean The margin of error is 2018 Cengage Learning May not be scanned copied or duplicated or posted to a publicly accessible website in whole or in part except for use as permitted in a license distributed with a certain product or service orotherwise on a password protected website or school approved learning management system for classroom use Essentials of Modern Business Statistics 7e .
Interval Estimate of a PopulationMean KnownExample Lloyds Department storeInterval estimate of is 82 3 92.
78 08 to 85 29We are 95 confident that the interval contains the population mean 2018 Cengage Learning May not be scanned copied or duplicated or posted to a publicly accessible website in whole or in part except for use as permitted in a license distributed with a certain product or service orotherwise on a password protected website or school approved learning management system for classroom use Essentials of Modern Business Statistics 7e .
Using Excel to construct a confidence interval Known Excel Formula WorksheetNote Rows 18 99are not shown 2018 Cengage Learning May not be scanned copied or duplicated or posted to a publicly accessible website in whole or in part except for use as permitted in a license distributed with a certain product or service or.
otherwise on a password protected website or school approved learning management system for classroom use Essentials of Modern Business Statistics 7e Using Excel to construct a confidence interval Known Excel Value WorksheetNote Rows 18 99.
are not shown 2018 Cengage Learning May not be scanned copied or duplicated or posted to a publicly accessible website in whole or in part except for use as permitted in a license distributed with a certain product or service orotherwise on a password protected website or school approved learning management system for classroom use Essentials of Modern Business Statistics 7e Interval Estimate of a Population Mean Known.
Example Lloyds Department storeConfidence level Margin of Error Interval estimate90 3 29 78 71 85 2995 3 92 78 08 85 9299 5 15 76 85 87 15.
In order to have a higher degree of confidence the margin of error and thusthe width of the confidence interval must be larger 2018 Cengage Learning May not be scanned copied or duplicated or posted to a publicly accessible website in whole or in part except for use as permitted in a license distributed with a certain product or service orotherwise on a password protected website or school approved learning management system for classroom use Essentials of Modern Business Statistics 7e .
Interval Estimate of a Population Mean KnownAdequate Sample Size In most applications a sample size of n 30 is adequate If the population distribution is highly skewed or containsoutliers a sample size of 50 or more is recommended .
If the population is not normally distributed but is roughlysymmetric a sample size as small as 15 will suffice If the population is believed to be at least approximately normal a sample size of less than 15 can be used 2018 Cengage Learning May not be scanned copied or duplicated or posted to a publicly accessible website in whole or in part except for use as permitted in a license distributed with a certain product or service or.
otherwise on a password protected website or school approved learning management system for classroom use Essentials of Modern Business Statistics 7e Interval Estimate of a Population Mean Unknown If an estimate of the population standard deviation s cannot bedeveloped prior to sampling we use the sample standard deviation.
s to estimate s This is the s unknown case In this case the interval estimate for m is based on the t distribution We ll assume for now that the population is normally distributed 2018 Cengage Learning May not be scanned copied or duplicated or posted to a publicly accessible website in whole or in part except for use as permitted in a license distributed with a certain product or service or.
otherwise on a password protected website or school approved learning management system for classroom use Essentials of Modern Business Statistics 7e t Distribution William Gosset writing under the name Student is the founder ofthe t distribution .
Gosset was an Oxford graduate in mathematics and worked for theGuinness Brewery in Dublin He developed the t distribution while working on small scalematerials and temperature experiments 2018 Cengage Learning May not be scanned copied or duplicated or posted to a publicly accessible website in whole or in part except for use as permitted in a license distributed with a certain product or service or.
otherwise on a password protected website or school approved learning management system for classroom use Essentials of Modern Business Statistics 7e t Distribution The t distribution is a family of similar probability distributions A specific t distribution depends on a parameter known as the.
degrees of freedom Degrees of freedom refer to the number of independent pieces ofinformation that go into the computation of s 2018 Cengage Learning May not be scanned copied or duplicated or posted to a publicly accessible website in whole or in part except for use as permitted in a license distributed with a certain product or service orotherwise on a password protected website or school approved learning management system for classroom use .
Essentials of Modern Business Statistics 7e t Distribution A t distribution with more degrees of freedom has less dispersion As the degrees of freedom increase the difference between the tdistribution and the standard normal probability distribution.
becomes smaller and smaller 2018 Cengage Learning May not be scanned copied or duplicated or posted to a publicly accessible website in whole or in part except for use as permitted in a license distributed with a certain product or service orInterval Estimate of a Population Mean: s Known Interval Estimate ofm. 𝑥± 𝑧𝛼/2𝜎𝑛. where: 𝑥 is the sample mean. 1 - is the confidence coefficient

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