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##### UMKC STAT235 Practice Comprehensive Final

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Question;Practice Comprehensive Final, STAT 235;Eleven Problems with a total of 100 points;1. The commute time for 19 UMKC faculty was collected and is;displayed in the stem-leaf plot below.;1;7;9;2;0;1;1;1;1;3;3;4;6;8;9;3;1;2;3;5;6;4;0;The following correpsonding calculations are based on the same;dataset;X X X;x = 500 x2 = 13944 (x x)2 = 786:1053;(a);(2 points) What;is the sample average?;(b);(2 points) What;is the sample median?;(c);(2 points) Is;there a mode, if so, what is it?;(d);(2 points) Approximate;the 25th percentile (i.e. Q1).;(e);(2 points) What;is the sample standard deviation?;(f);(2 points) What;is the percentile rank of the value 33?;(g);(2 points) What;can you say about the percentage of the data that lies within 2-standard;deviations of the mean?;2.;The number of;siblings of a class of students has the following distribution.;Siblings X;0;1;2;3;4;p(x);.200;.455;.245;.075;.025;Suppose a student is picked at random from the class. Let X denote;the number of siblings of the student. Then, X has the above distribution.;(a);(2 points) What;is the chance that the student picked at random has two or more siblings?;(b);(2 points) What;is the expected number of siblings for the student?;(c);(3 points);Determine Var(X) and SD(X).;3.;A study conducted;by the Department of Health and Human Service reported that 15% of adults su er;from migraine headache. To test the validity of this statement, 68 randomly;selected adults are interviewed. Let X be the number of adults su ering from;migraine headache in the sixty-eight interviewees. Assume that there are 15% of;adults with migraine headache. Answer the following questions.;(a);(3 points);Justify that X is a binomial random variable and identify the n and p.;(b);(2 points);Compute the mean and standard deviation of X.;(c);(2 points) What;distribution can approximate the distribution of X? (Be speci c about;parameters.);(d);(2 points) What;is the probability that at least 15 adults su ering from migraine headache in;the 68 interviewees?;4.;Suppose that the;cholesterol level of women at ages 20{29 is normally distributed with a mean;level 185 (in mg/dL) and standard deviation 36.5 (in mg/dL). Let X be the;cholesterol level of a randomly selected women at ages 20{29.;(a);(1 point) What is;the distribution of X?;(b);(2 points) What;is the probability that the cholesterol level of the randomly selected woman is;more than 200?;Suppose 16 women;are picked at random. Let X be the mean cholesterol level of them.;1;(c) (2 points) Determine the expected value, the standard deviation of;the sample mean cholesterol level, X, and its distribution.;(d);(2 points) Find;the probability that the sample mean cholesterol level is more than 200.;5.;(4 points) The;management of a supermarket wants to adopt a new promotional policy giving a;free gift to every customer who spends more than a certain amount of per visit;at this supermarket in the holiday season. The expectation of the management is;that after this promotional policy is advertised, the expenditures for all;customers at this supermarket will be normally distributed with a mean of $95;and a standard deviation of $21. If the management wants to give free gifts to;at most 8% of the customers, what should be the amount be above which a;customer would receive a free gift?;6.;Nielsen Media;Research wishes to estimate the mean number of hours that high school students;spend watching TV on a weekday. For 99% con dence interval, the margin of error;at 0.25 hour is desired. Past studies suggest that a population standard;deviation of 1.7 hours is reasonable.;(a);(1 point) What is;the maximum error Nielsen Media Research allows?;(b);(2 points);Estimate the minimum sample size required to estimate the population mean with;the stated accuracy at 99% con dence level.;7.;The past records;of a supermarket show that its customers spend an average of $65 per visit at;this store. Recently the management of the store initiated a promotional;campaign according to which each customer receives points based on the total;money spent at the store and these points can be used to buy products at the;store. The management expects that as a result of this campaign, the customers;should be encouraged to spend more money at the store. To check whether this is;true, the manager of the store took a sample of 12 customers who visited the;store. The following data give the money (in dollars) spent by these customers;at this supermarket during their visits.;88 69 141 28 106 45 32 51 78 54 110 83;Assume that the money spent by all customers at this supermarket;has a normal distribution. Answer the following questions.;(a);(2 points);Compute the mean and the standard deviation of the above sample.;(b);(1 point) De ne;the of interest in the context of this;problem.;(c);(2 points);Construct a 90% con dence interval for.;What is the con dence based on?;(d);Is the mean;amount of money spent by all customers at this supermarket is higher than $65;after the campaign? Perform the hypothesis testing at 1% signi cance level by;answering the following questions.;i.;(1 point);Formulate the null and alternative hypothesis.;ii.;(2 points) State;the test statistic and its approximate distribution.;iii.;(2 points);Determine the critical value for =:01;and state the decision rule.;iv.;(1 point);Calculate the observed value of the test statistic from the sample.;v.;(1 point) State;whether H0 is rejected and tell why.;8.;According to a;survey, the mean price of gasoline in U.S was 1.20 in 1998 and 1.10 in per;gallon in 1997. Suppose that these means were based on random samples of 100;gas stations for 1998 and 120 gas stations for 1997. Also, assume that the;sample standard deviations were $.11 for 1998 and $.10 for 1997. Answer the;following questions.;(a);(1 point) Let1 and2 be the mean prices per;gallon of gasoline in U.S in 1998 and 1997. What is the point estimate for the1 2?;(b);(2 point);Construct a 94% con dence interval for 1 2.;(c);Is the gasoline;price was higher in 1998 than in 1997? Perform a hypothesis testing at 6% signi;cance level by answering the following questions.;2;i. (1 point) Formulate the null and alternative hypothesis.;ii. (2 points) State the test statistic and its approximate;distribution.;iii. (2 points) Determine the;critical value for =:06 and state the decision rule. iv. (1 point) Calculate;the observed value of the test statistic from the sample. v. (1 point) State;whether H0 is rejected and tell why.;vi. (2 points) Compute the P-value and do the hypotheses testing;based on the P-value.;9. Three years ago, a poll;conducted by Louis Harris & Associates for Business Week magazine, examined;the perception of American adults of their government. When asked whether the;U.S. government represents the concerns of the American people or those of;special interest groups, 63% of those polled felt that the U.S. government;primarily represents the concerns of special interest groups. Assume that this;percentage was true for the population of all American adults at the time the;poll was conducted. A recent random sample of 1200 American adults found that;61% of them feel that the U.S. government represents the concerns of special interest;groups. Let p be the percentage of all American adults who hold this view;recently. Answer the following questions.;(a) (2 points) What is the point estimate for the p? What is the;margin of error?;(b) (2 points) Construct a 96% con dence interval for p. Is p;included in this interval?;(c) Is the currant proportion of;all U.S. adults who hold this opinion is less than 63%? Perform the hypothesis;testing at 1% signi cance level by answering the following questions.;i. (1 point) Formulate the null and alternative hypothesis.;ii. (2;points) State the test statistic and its approximate distribution.;iii. (2 points) Determine the;critical value for =:01 and state the decision rule. iv. (1 point) Calculate;the observed value of the test statistic from the sample. v. (1 point) State;whether H0 is rejected and tell why.;10. A company has two restaurants;in two di erent areas of Kansas City. The company wants to estimate the;percentages of patrons who think that the food and service at each of these;restaurants are excellent. A sample of 200 patrons taken from the restaurant in;area A showed that 118 of them think that the food and service are excellent at;this restaurant. Another sample of 250 patrons taken from the restaurant in;area B showed that 160 of them think that the food and service are excellent at;this restaurant. Let p1 and p2 be the population proportions of patrons to the restaurant in;Area A or B who think the food and service are excellent. Answer the following;questions.;(a) (1 point) What is the point estimate for the p1 p2?;(b) (2 point) Construct a 94% con dence interval for p1 p2.;(c) Is the proportion of patrons at the restaurant in area A who;think that the food and service are excellent is lower than the corresponding;proportion at the restaurant in the area B? Perform a hypothesis testing at 6%;signi cance level by answering the following questions.;i. (1 point) Formulate the null and alternative hypothesis.;ii. (2 points) State the test statistic and its approximate;distribution.;iii. (2 points) Determine the;critical value for =:06 and state the decision rule. iv. (1 point) Calculate;the observed value of the test statistic from the sample. v. (1 point) State;whether H0 is rejected and tell why.;11. The;following table gives information on the temperature in Kansas City and the;volume of ice cream (in pounds) sold at an ice cream parlor for a random sample;of eight days during a recent summer.;Temperature;93;86;77;89;98;102;87;79;Ice cream sold;202;175;123;198;232;267;158;117;Take temperature as a predictor;and volume of ice cream sold as a response. Answer the following questions;based on the following part of the Minitab Computer output.;3;The regression equation is;icecream = - 337 + 5.86 temp;Predictor;Coef;Stdev;t-ratio;p;Constant;-336.80;42.91;-7.85;0.000;temp;5.8599;0.4808;12.19;0.000;s = 10.99;R-sq = 96.1%;(a);(1 points) Plot;the scatter diagram and the regression line.;(b);(2 point);Construct a 95% con dence interval for the intercept, 0.;(c);(1 point) What is;the implication for the relationship of the volume of ice cream sold and the;temperature when1 = 0?;(d);Test H0;: 1;= 0, versus H1: 1;6= 0 at 1% signi cance level based on;i);(2 points) T-test;statistic;ii);(2 points) on;P-value.;(e);(1 point) What is;the estimate for, the standard;deviation of the error?;(f);(2 point) What is;the value of the correlation coe cient, r? Is the linear relationship between;the volume of ice cream sold and the temperature strong? Tell why.;(g);(1 point) Predict;the volume of ice cream sold when the temperature is 100 degree.

Paper#62158 | Written in 18-Jul-2015

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