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Z=Assume normally distributed populations with unknown standardSalesBeforeAfter@4) Four people were given extensive sales training. Test whether#tTest: Paired Two Sample for MeansVarianceObservationsPearson Correlationdft StatP(T<=t) onetailt Critical onetailP(T<=t) twotailt Critical twotail<The null hypothesis is rejected as the tvalue from the dataQuick's Answers:=of 4.243 is beyond the t critical value of 2.353. Training %increased employee sales performance.5Additional Practice Problems are located on 5 sheets.Sheet 2 Probability Test*Sheet 3 Inferential Statistics Part 1 Test*Sheet 4 Inferential Statistics Part 2 Test'Sheet 5 Correlation and Regression Test7of this book may be viewed at www.businessbookmall.com.6=chapters and their numbers are from said book. Sample pages ;practice calculating statistics using Microsoft (TM) Excel.&:=Problems, data sets, and key answers are provided. Directions<Problems, with slight modifications, and data sets have beenACopyright laws prohibit the reproduction and transmission of thisFmaterial or any portion of this material in any form and by any means BDisks may be copied for educational purposes for a reasonable fee.,Contact Walter Antoniotti at 18002536595.Additional Practice Problems 28taken from the Tests of Statistics (ISBN 0963277251) of "6The Quick Notes Learning System (TM) series. Names of $#Sheet 1 Descriptive Statistics TestDand Cumulative Relative Frequency Distribution with the first class Hhaving class limits of 50  59 and the remaining classes of equal width.DataRangebins61A) Make an array and calculate a range for this data.E) Standard DeviationB2) Use this sample data when calculating the following statistics.Data MeanStandard ErrorMedianModeStandard DeviationSample VarianceKurtosisSkewnessMinimumMaximumSumCount31) Average hours worked by manufacturing workers is Test 1 on Descriptive StatisticsS DZ Quick's Answers:zSt DevLLUL>mean of 15 hours per week and a standard deviation of 3 hours.<A) How many hours must be spent studying to be in the top 1%+of the students attending State University?99th %B) Calculate the fourth decile.xp(x)Cumm PrC) State the entire probability distribution.>to have approximately 5% defective parts. Assuming a Binomial Faverage refreshment spending of $7.60. The standard deviation for theHW,95% Gpopulation is $2.10. Calculate the 95% and 98% confidence interval for:average refreshment spending by fans attending this game. HW,98% " P(41.75 hours < = x < 42 hours) =#C) P(41.75 hours < = x < 42 hours)!A) P(41 hours < = x < 42.5 hours)"P(39.5 hours < = x < 42.5 hours) =P(x < = 1) =A) Top 1% is > = 22 hoursin column C and D.Do your calculations SpendRange =?revealed average refreshment spending of $7.60. The population?standard deviation was $2.10. The makers of Dud beer will not Edistribute their product to a ballpark unless it is possible that thehypothesizedpopulation meanalphasample meansample standard deviationcountz from data AWe fail to reject the null hypothesis because z from the data, critical value for z?1) A sample of 36 out of 25,000 baseball fans attending a game >3) ABC Company is questioning whether the quality of material =coming from the company's three suppliers has something to do?20 production runs for each supplier were counted. Using a .05Blevel of significance, determine whether the number of defects andCwith the number of defective products. The number of defects from Co 2Co 1Co 3High DefectsLow DefectsTotals Observed Outcomes SupplierspvalueMaterials SuppliersEtheir sales performance improved using a .05 level of significance. Store AStore BzTest: Two Sample for MeansKnown VarianceP(Z<=z) onetailz Critical onetailP(Z<=z) twotailz Critical twotail?seconds and a standard deviation of 8 seconds. A sample of 49 A7) Samples of 10 taken in 1985 and 1995 revealed the average time>people spend grocery shopping decreased from 18 minutes to 14 FTest TwoSample for VariancesFP(F<=f) onetailF Critical onetail:Accept the null hypothesis as the Fvalue from the data ofsame.:Note: Because Excel assumes onetail, enter .05 for alpha.Employee Efficiency RatingMethod 1Method 2Method 3Anova: Single FactorSUMMARYGroupsAverageANOVASource of VariationSSMSPvalueF critBetween Groups
Within GroupsTotal:Reject the null hypothesis as the Fvalue from the data ofthe null hypothesis.@5.77 is beyond the F critical value of 4.26. The mean efficiency'of employees differs for the 3 methods.?Note the pvalue of 0.024 is below .05 indicating rejection of Dthat the difference in average efficiency of Department 1 (6.0) and <The Quick Notes Learning System (TM) series. In that book a $st error of meanHypothesized DifferenceVar2) coefficient of correlation3) coefficient of determination"4) coefficient of nondetermination36) .05 level of significance test for slope being 07) regression equationC1) Answer the following questions using this data that was gathered;to determine whether research and development expenditures 2Begin scatter in B20 and your calculations in B30.2affect profit. Figures are in millions of dollars.Profit R&D Regression Statistics
Multiple RR SquareAdjusted R Square
RegressionResidual InterceptSignificance F Lower 95% Upper 95%6RSquared, 0.784 is the coefficient of determination. 4It shows that 78.4% of the variability of profit is 3Coefficient of nondetermination, 1  RSquared, is "accounted for by R&D variability. 2in profit is not accounted for by R&D variability.7Standard error of 9.543641 indicates the average error #in predicting profit is $9,543,641.1Anova pvalue of 0.019 is below the .05 level of 1Intercept coefficient of 13.5 is the yintercept.&R&D coefficient of 6.54 is the slope.*Regression equation is Y.x = 13.5 + 6.54x.
)8) expected profit for R&D of $8,000,000.St ErrRegression of R&D and Profit41) scatter diagram with R&D the independent variable&5) average error for predicting profit<Multiple R, the coefficient of correlation of 0.885 is high.
>1  .78357 = 0.21643. It shows that 21.6% of the variability the slope could be zero.3significance so we reject the null hypothesis that 2Problem numbers are from The Quick Notes Learning /System (TM) for Statistics, ISBN 0963277251.Not all the problems will be done with Excel.@the .01 level of significance whether this ballpark qualifies to8receive Dud beer. See cell A8 of sheet 7 for directions.7Cnegative 1.143, is not beyond the critical value for z of  2.326. B8the company supplying materials are related (dependent).Baverage time to serve customers at two of their stores. A sample @seconds and a standard deviation of 7 seconds. Test at the .02 Alevel of significance whether the mean time to wait on customers DResults: The z from the data of 2.89 is beyond the critical value ofWaiting time differs.ENote that 2.89 is also beyond 2.05, the critical value for a onetail@Note that the pvalues of 0.0019 from onetail and 2 X 0.0019 =B0.0039 for twotails are both lower than alpha of .02. This means Gthe difference between these means is large and the tail or tails are #small relative to the alpha of .02.@1.58 is not beyond the F critical value of 3.18. Variance is the?5) Owners of the Quick Chow Restaurant are concerned about the '4In said book, sample pages of which may be viewed at>www.businessbookmall.com, a number of nonparamet<ric tests are Esecond part of this question proved at the .01 level of significance CDepartment 3 (8.5) could be zero at the .01 level of significance. Hours(Pthere is enough of a difference between the observed frequency9and the expected frequency to reject the null hypothesis.%8.05 level of significance. ;Defects and materials suppliers are not independent at the 'test so store A is slower than store B.5Problems 6 of Statistics will not be done with Excel.<minutes. Respective standard deviations were 5 minutes and 45Problems 8 of Statistics will not be done with Excel.>These test questions came from Statistics (ISBN 0963277251) of*,covered by the Inferential Statistics Test. $Begin your calculations in cell B72.$Test 4 on Correlation and RegressionCoef*Expected profit for R & D of $8,000,000 is'See cell A7 of sheet 11 for directions.8They should be done after the problems in the file Quick3# Statistics Using Microsoft"! Excel. !H1B) Using this data, make a 4class Frequency Distribution, Histogram, ?Answers: Range is 84  53 = 31 and bins are 59, 69, 79, and 89.$D) P(39.5 < = x < 42 hours) = 0.9973!B) Fourth Decile is 13.4 to 14.2.Quick's Answers Using fxHW,95%HW,98%Quick's Answers Using DataDNote: For these problems, use the actual data and not the problem's rounded statistics.@Note: This is really the same problem as problem 15 of sheet 2. CAt that time we knew $8.00 was possible at the .01 level for a one=tail test because the 98% confidence interval included $8.00.Your Analysis:Quick's Analysis:=Quick's Analysis: The answer of a pvalue of 0.015 indicates we reject the null hypothesis. Quick's Analysis:@2.33 for this twotail test and we reject the null hypothesis. #Cof 32 customers from store A resulted in a mean service time of 80 =customers from store B resulted in a mean service time of 75 Aminutes. Test at the .10 level of significance whether there has ,been a change in shopping time variability. ?Note the pvalue of 0.39 is substantially above .01 indicating ?strong acceptance (failure to reject) of the null hypothesis. Shopping Time<quality were compared for three computer component assembly =9) Employee efficiency based upon production time and product<methods by Insel Corporation. Use ANOVA analysis to test at >the .05 level of significance whether mean employee efficiency%of these assembly methods are equal. <Note: The pvalue of 0.012 is below alpha of .05, and again
'See cell A7 of Answers3 for directions.)See cell A60 of Answers 5 for directions.(See cell A7 of Answers 5 for directions.)See cell A29 of Answers 5 for directions.LDirections are in Answers 11 of Quick Statistics Using Microsoft (TM) Excel.)See cell A27 of Answers 3 for directions.)See cell A89 of Answers 5 for directions.*See cell A137 of Answers 9 for directions.+See cell A81 of Answers 9 for directions. )See cell A62 of Answers 9 for directions.!at these two stores is the same. Begin your answer in cell B46.)See cell F7 of Answers 7 for directions. deviations. *See cell A34 of Answers 9 for directions. Quick's Scatter Diagram=on how to do the problems are not provided. For those wantingBassistance, a link to Quick Statistics Using Microsoft (TM) Excel $(ISBN 192985000X) has been provided.Expecter OutcomesB) P(x < 40.345 hours)P(x < 40.345 hours) =B) P(x < 40.345 hours) = 0.0951F11) Five parts are to be inspected from a production process designed bkGl
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