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Quantitative Methods
QMS 202
Clare Chua

Confidence Interval What is unknown Population Mean and Population proportionEstimateWhat is known Sample mean and sample proportionCan take a sample of quantitative data and calculate the sample mean Use this sample mean to construct an interval that will contain the population What Population Parameter are mean c of the time you testingc ie 95 90 92 etcconfidence that this interval will contain the true NonIs p normalIsnormalpopulation meanStandarIenp5 IeX is or can be We use this c to calculate the z and t values known as critical values where d and n1passumed normal or this c is treated as area under the curveprocedu5n 30CLT re To find Z values use INVN function and input area which is the Theorem requiredconfidence level usually expressed instd dev1 and mean0 To find the t values you have two options 1 t table which will be Isprovided in the quiztestexam and 2 INVt function and input upper knownarea df degree of freedomn1Limits If you are asked to construct a 95 confidence interval for population parameter you use INTR sometimes variance will be give for instance 29 but 3Limits Limits tdistribution is a continuous probability distribution that resulted from estimating the mean of a small sample size and the population standard deviation is unknown more spread out than a normal distribution the larger the degrees of freedommore accurate normal distributionLimits Estimation using sample data to estimate the unknown population parameterorLimits Confidence interval an interval that is likely to include a population parameterorgiven a confidence level usually expressed in percentage Find Sample Margin of error measures the uncertainty in estimating the population parameter SizeMargin of error critical value x standard error Example 1Example 2A sample of 20 students were asked to fill in a survey on gender how many The director of patient services of a large health hours spent studying for the test and what was the grade earned on the same maintenance organization wants to evaluate patient test that they had studied forwaiting time at a local facilityA random sample of Hours Male 14 Female 17 Female 3 Female 6 Male 17 Male 3 Male 8 Male 25 patients is selected from the appoint bookThe 4 Female 20 Male 15 Female 7 Male 9 Male 0 Male 5 Female 11 Female 15 waiting time is defined as the time from when the Male 18 Female 13 Male 8 Male 4patient signs in to when he or she is seen by the Construct a 91 confidence interval estimate of the proportion of all female doctorThe following data represents the waiting studentstimes in minutesx is knowna What parameter are you estimating here1930453929411317410b Statecheck the necessary assumptions required to construct the confidence interval 556863872521285225393619np5 20 8208 4860406n1p20 18201245421226491231431The conditions are met therefore it is normally distributed951171c Before you construct a 91 confidence interval estimate of the proportion of all female students state the critical value z 16954 Construct a 95 confidence interval estimate of the InvN Area 091 1 0popavg waiting timed The point estimate for a 91 confidence interval estimate of the proportion of all 1 State the necessary assumptionsconditions required female students is x985to construct a 95 confidence interval estimate for the e State the 91 confidence interval estimate of the population proportion of all female population average waiting time It is not normally distributed n is not equal or Example 3greater than 30 A survey is planned to determine the mean annual family medical expenses ofApply CLT no because n25employees of a large companyThe management of the company wishes to beAssume x is normally distributed 95 confident that the sample mean is correct to within 50 of the population 2State the critical value needed to construct the 95 mean annual family medical expensesA previous study indicates that the confidence interval estimate for the population average standard deviation is approx 400waiting time a How large a sample size is necessary2458246In this question you are t critical values 2064 Calc Dist t Invt Area estimatingthe mean0025 df 24z19599 e50 400nz eb If management wants to be correct with 25 how many employees need to be selected 9833984 z19599 e25 400 3 State the point estimate and its value used to construct a Example 495 confidence interval estimate for the population What proportion of people hit snags with online transactionsAccording to a poll average waiting time 89 hit snags with online transactionsa To conduct a follow up study that would provide 95 confidence that the point estimate is x27892 Calc INTR t 1s List Clevel 095correct to within 004 of the population proportion how large a sample size is required 4The 95 confidence interval estimate for the population 2350339234 In this question you are estimatingthe proportion average waiting time is 221668939336171261089 z19599 e004 if error of margin not given use 005Calc INTR t 1s List Clevel 095 left and right Hypothesis TestingMean n 1 zTTestHypothesis TestingMean ZTest A new battery has beenA new battery has been developed to developed to power laptop power laptop computers It will sell in a computers It will sell in a certain price range It is hoped that the certain price range It is battery can be used for more than 400 hoped that the battery hours before it needs to be recharged We can be used for more than will assume that the battery lives are 400 hours before it needs normally distributed with a standard to be recharged We will deviation of 025 hours A random sample assume that the battery of 50 batteries is tested The sample lives are normally batteries lasted an average of 412 hours distributed A random before they required recharging Use a sample of 50 batteries is significance level of 5 Can we conclude tested The sample batteries lasted an average of 412 hours Is and1 2known 1 2
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