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Department
Quantitative Methods
Course
QMS 202
Professor
Clare Chua
Semester
Winter

Description
Example 1Confidence IntervalTo find Z values use INVN function and input area which is the A sample of 20 students were asked to fill in a confidence level usually expressed instd dev1 and mean0 survey on gender how many hours spent studying for the test and what was the grade earned on the To find the t values you have two options 1 t table which will be provided same test that they had studied forin the quiztestexam and 2 INVt function and input upper area df Hours Male 14 Female 17 Female 3 Female 6 degree of freedomn1Male 17 Male 3 Male 8 Male 4 Female 20 Male tdistribution is a continuous probability distribution that resulted from estimating the 15 Female 7 Male 9 Male 0 Male 5 Female 11 mean of a small sample size and the population standard deviation is unknown more Female 15 Male 18 Female 13 Male 8 Male 4spread out than a normal distribution the larger the degrees of freedommore accurate Construct a 91 confidence interval estimate of the normal distributionproportion of all female studentsMargin of error measures the uncertainty in estimating the population parameter a What parameter are you estimating hereMargin of error critical value x standard error b Statecheck the necessary assumptions required to Point estimate Using the sample statistic eg or p to estimate the corresponding Example 2construct the confidence interval The director of patient services of a large health Example 4np5 20 8208 maintenance organization wants to evaluate What proportion of people hit n1p20 182012patient waiting time at a local facilityA random snags with online The conditions are met therefore it is normally sample of 25 patients is selected from the appoint transactionsAccording to a distributedbookThe waiting time is defined as the time poll 89 hit snags with c Before you construct a 91 confidence interval from when the patient signs in to when he or she online transactionsestimate of the proportion of all female students state the is seen by the doctorThe following data a To conduct a follow up study critical value z 16954 represents the waiting times in minutesx is that would provide 95 InvN Area 091 1 0knownconfidence that the point d The point estimate for a 91 confidence interval 1930453929411317410estimate is correct to within estimate of the proportion of all female students is x55686387004 of the population 9852521285225393619Example 3proportion how large a sample 4860406A survey is planned to determine the mean annual size is required 45421226491231431family medical expenses of employees of a large 2350339234 In this 951171companyThe management of the company wishes question you are estimating to be 95 confident that the sample mean is Construct a 95 confidence interval estimate ofthe proportion correct to within 50 of the population mean the popavg waiting time089 z19599 e004 annual family medical expensesA previous study 1 State the necessary assumptionsconditions Hypothesis TestingMean ZTestindicates that the standard deviation is approx required to construct a 95 confidence interval A new battery has been developed 400estimate for the population average waiting timeto power laptop computers It willIt is not normally distributed n is not equal or a How large a sample size is necessary2458246sell in a certain price range It is greater than 30 In this question you are estimatingthe meanhoped that the battery can be usedApply CLT no because n25z19599 e50 400nzfor more than 400 hours before itAssume x is normally distributedeneeds to be recharged We will 2State the critical value needed to construct the 95 b If management wants to be correct with 25 how assume that the battery lives are confidence interval estimate for the population average many employees need to be selected normally distributed with a waiting time standard deviation of 025 hours A t critical values 2064 Calc Dist t Invt random sample of 50 batteries is Area 0025 df 24tested The sample batteries lasted an average of 412 hours before they required recharging 3 State the point estimate and its value used to construct a 95 confidence interval estimate for the population average waiting time x27892 Calc INTR t 1s List Clevel 0954The 95 confidence interval estimate for the SPSS Examplepopulation average waiting time is 221668939The table below is a random sample of 20 companies whose 336171261stock is traded on the New York Stock Exchange For each Calc INTR t 1s List Clevel 095 left and right company the number of shares traded on May 25 1999 and values May 26 1999 is given Hypothesis TestingMean TTesta At the 05 level of significance is there evidence that the A new battery has been developed to power average number of shares traded on May 25 is higher than the laptop computers It will sell in a certain price average number of shares traded on May 26 range It is hoped that the battery can be used for b Determine the pvalue in amore than 400 hours before it needs to be recharged We will assume that the battery lives are normally distributed A random sample of 50 batteries is tested The sample batteries lasted an average of 412 hours with a standard deviation of 025 hours before they required recharging Let Hypothesis Testing for Z Test knownA company that makes bolts that are used on an automotive component uses two machines to make these bolts It has been determined by past studies that the standard deviation of the bolt diameters made by machine 1 is 0025 mm and the standard deviation of the bolt diameters of machine 2 is 0022 mm Both machines have a dial to set for the desired diameter Recently they used both machines to fill a large order Ho D0The customer found that many of the bolts from a Ha D0 certain package were too large and made a complaint Assume the distribution of the differences between the It was determined that the package in question was number of shares traded on the two days is at least made by machine 2The manufacturer decided to take approximately normally distributed samples of the bolts from both machines to test to see Decision Rule Reject Ho if pvalue isthan the level of whether the mean diameter of the bolts from machine 2 significance 005 otherwise fail to reject Ho was significantly larger than the mean diameter from pvalue04645 machine 1 when the dial was set to the same diameter Calc TEST t 1s0 0 0 x 6090 sx 30199799 n 20on each machineThe sample of 100 bolts from Decision Fail to reject Homachine 1 had a mean diameter of 5023 mm and a Is and1 2known 1 2
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