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DeVry Kansas City STATS221, Fall 2014 summer




Question;Final Exam;Review Questions;Solutions Guide;You will;probably want to PRINT THIS so you can carefully check your answers. Be sure to;ask your instructor if you have questions about any of the solutions given;below.;1.Explain the difference between a population and a sample. Inwhich;of these is it important to distinguish between the two in order to use the;correct formula? mean, median, mode, range, quartiles, variance, standard;deviation.;2.The following numbers represent the weights in pounds of six 7-year;old children in Mrs. Jones' 2nd grade class.;{25, 60, 51, 47, 49, 45};Find the mean, median, mode, range, quartiles;variance, standard deviation.;3.If the;variance is 846, what is the standard deviation?;4.If we;have the following data;34, 38, 22, 21, 29, 37, 40, 41, 22, 20, 49, 47;20, 31, 34, 66;Draw a stem and leaf. Discuss the shape of the;distribution.;5.What;type of relationship is shown by this scatter plot?;45;40;35;30;25;20;15;10;5;0;0;5;10;15;20;6.What values can r take in linear regression?;Select 4 values in thisinterval and describe how they would be;interpreted..;7.Does correlation imply causation?;0;8. To predict the annual rice yield in pounds we use;the equation;y?=859+5.76x1+3.82x2, where x1 represents the number of acres;planted (in thousands) and where x2 represents;the number of acres harvested (in thousands) and where r2 =.94.;a);Predict;the annual yield when 3200 acres are planted and 3000 are harvested.;b);Interpret;the results of this r2 value.;c);What do we;call the r2 value?;10.The Student Services office did a survey of 500;students in whichthey asked if the student is part-time or full-time.;Another question asked whether the student was a transfer student. The results;follow.;Transfer Non-Transfer Row Totals;Part-Time;100;110;210;Full-Time;170;120;290;Column Totals 270;230;500;a);If;a student is selected at random (from this group of 500 students), find the;probability that the student is a transfer student. P (Transfer);b);If;a student is selected at random (from this group of 500 students), find the;probability that the student is a part time student. P (Part Time);c) If a student is selected at random (from this;group of 500 students), find the probability that the student is a transfer;student and a part time student. P(transfer?part time).;d) If a student is selected at random (from this;group of 500 students), find the probability that the student is a transfer;student if we know he is a part time student. P(transfer | part time).;e) If a student is selected at random (from this group;of 500 students), find the probability that the student is a part time given he;is a transfer student. P(part time | transfer);f) Are the events part time and transfer;independent? Explain mathematically.;g) Are the events part time and transfer mutually;exclusive. Explain mathematically.;Solution: (a;11.A shipment of 40 television sets contains 3 defective units. Howmany;ways can a vending company can buy five of these units and receive no defective;units?;12.How do;you recognize a discrete distribution?;13.The random variable X represents the annual;salaries in dollars ofa group of teachers. Find the expected value;E(X).;X = {$35,000, $45,000, $55,000}.;P(35,000) =.4, P(45,000) =.3, P(55,000) =.3;14.How do;you recognize a binomial experiment?;15.An advertising agency is hired to introduce a new product. Theagency;claims that after its campaign 61% of all consumers are familiar with the;product. We ask 7 randomly selected customers whether or not they are familiar;with the product.;a) Is this a binomial experiment? Explain how you know.;b) Use the correct formula to find the probability;that, out of 7 customers, exactly 4 are familiar with the product. Show your;calculations.;16.How do;you recognize a Poisson experiment?;17.The mean number of cars per minute going through;theEisenhower turnpike automatic toll is about 7. Find the probability;that exactly 3 will go through in a given minute using the correct table;formula, or Excel function.;18.How do;you recognize a normal distribution?;19. Label the following as continuous or discrete;distributions.;a);The;lengths of fish in a certain lake.;b);The;number of fish in a certain lake.;c);The;diameter of 15 trees in a forest.;d);How;many trees are on a farmer's acre.;20.Jack weighs 160 pounds and his sister weighs 110;pounds. If themean weight for men his age is 175 with a standard;deviation of 14 pounds and the mean weight for women is 145 with a standard;deviation of 10 pounds, determine whose weight is closer to;average." Write your answer in terms of z-scores and areas under the;normal curve.;21.On a dry surface, the braking distance (in meters) of a certain car;is a normal distribution with mu =? = 45.1 m and sigma =? = 0.5;(a) Find the braking distance that corresponds to z =;1.8;(b) Find the braking distance that represents the;91st percentile.;(c) Find the z-score for a braking distance of 46.1 m;(d) Find the probability that the braking distance is;less than or equal to 45 m;(e) Find the probability that the braking distance is;greater than 46.8 m;(f);Find;the probability that the braking distance is between 45 m and 46.8 m.;5;21.;A;drug manufacturer wants to estimate the mean heart rate for patients with a;certain heart condition. Because the condition is rare;the;manufacturer can only find 14 people with the condition currently untreated.;From this small sample, the mean heart rate is 101 beats per minute with a;standard deviation of 8.;(a) Find a 99% confidence interval for the true mean;heart rate of all people with this untreated condition. Show your calculations.;(b) Interpret this confidence interval and write a;sentence that explains it.;23.Determine the minimum required sample size if you;want to be80% confident that the sample mean is within 2 units of the;population mean given sigma = 9.4. Assume the population is normally;distributed.;24.A social service worker wants to estimate the true proportion ofpregnant;teenagers who miss at least one day of school per week on average. The social;worker wants to be within 5% of the true proportion when using a 90% confidence;interval. A previous study estimated the population proportion at 0.21.;(a) Using this previous study as an estimate for p;what sample size should be used?;(b) If the previous study was not available, what;estimate for p should be used?;25.Suppose you are performing a hypothesis test on a claim about apopulation;proportion. Using an alpha =.04 and n = 90, what two critical values determine;the rejection region if the null hypothesis is Ho: p = 0.54?;(a) ? 1.96;(b) =? 2.05 (c) ? 2.33 (d) none of these;26.A restaurant claims that its speed of service time is less than 15minutes.;A random selection of 49 service times was collected, and their mean was;calculated to be 14.5 minutes. Their standard deviation is 2.7 minutes. Is;there enough evidence to support the claim at alpha =.07. Perform an;appropriate hypothesis test, showing each important step. (Note: 1st Step;Write Ho and Ha, 2nd Step: Determine Rejection Region, etc.)


Paper#61810 | Written in 18-Jul-2015

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