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##### STATS Problems with Solution

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Question;Refer to the following table for Questions 1, 2, and;3.Show all work. Just the answer, without;supporting work, will receive no;credit.;The table shows;temperatures on the first 12 days of October in a small town in Maryland.;Date;Temperature;Date;Temperature;Date;Temperature;Oct 1;73;Oct 5;53;Oct 9;66;Oct 2;65;Oct 6;52;Oct 10;49;Oct 3;65;Oct 7;62;Oct 11;52;Oct 4;70;Oct 8;55;Oct 12;57;1. Determine the;five number summary for this data.;The ordered data set is;49 52 52 53 55 57 62 65 65 66 70 73;2. Determine the;mean temperature;3. Determine the;mode(s), if any..;Refer to the following situation for Questions 4, 5, 6;and 7.Show all work. Just the answer, without;supporting work, will receive no;credit.;The frequency distribution below shows;the distribution for checkout time (in minutes) in UMUC MiniMart between 3:00;and 4:00 PM on a Friday afternoon.;Checkout Time;(in minutes);Frequency;1.0 ? 1.9;6;2.0 ? 2.9;7;3.0 ? 3.9;2;4.0 ? 4.9;3;5.0 ? 5.9;2;4.;What percentage of the checkout times was at least 4 minutes?;5.;Calculate the mean of this frequency distribution.;6.;Calculate the standard deviation of this frequency distribution.;Class;Midpoint;(x);Frequency;(f);d;= x - x-bar;f*d*d;1.0;- 1.9;1.45;6;-1.40;11.7600;2.0;- 2.9;2.45;7;-0.40;1.1200;3.0;- 3.9;3.45;2;0.60;0.7200;4.0;- 4.9;4.45;3;1.55;7.2075;5.0;- 5.9;5.45;2;2.60;13.5200;Total;20;34.3275;7.;Assume that the smallest observation in this dataset is 1.2 minutes. Suppose this;observation;were incorrectly recorded as 0.12 instead of 1.2. Will the mean increase;decrease, or remain the same? Will the median increase, decrease or remain the;same? Explain your answers.;Refer to the following information for Questions 8 and 9.Show all work. Just the answer, without supporting work, will receive no;credit.;A 6-faced die is rolled two;times. Let Abe the event that the outcome of the first roll is greater;than 4. Let Bbe the event that the outcome of second roll is an odd number.;8.What is the probability that;the outcome of the second roll is an odd number, given that the first roll is;greater than 4? (10 pts);9. AreAandBindependent? Why or;why not? (5 pts);Refer to the following data to answer questions 10 and 11.Show all work. Just the answer, without;supporting work, will receive no;credit.;A random sample of STAT200;weekly study times in hours is as follows: 4 14 15 17 20;10. Find;the standard deviation. (10 pts);11. Are;any of these study times consideredunusualin;the sense of our textbook? Explain.?Does this differ with your intuition? Explain. (5;pts);Refer to the following data to answer questions 12 and 13.Show all work. Just the answer, without;supporting work, will receive no credit.;There are 1500 juniors in a;college. Among the 1500 juniors, 200 students are taking STAT200, and 100;students are taking PSYC300. There are 50 juniors taking both courses.;12. What is the probability;that a randomly selected junior is in at least one of the two courses?;13. What is the;probability that a randomly selected junior takes only one of the two courses?;Refer to the following information for Questions 14, and 15.Show all work. Just the answer, without supporting work, will receive no;credit.;A box contains 10 chips. The;chips are numbered 1 through 10. Otherwise, the chips are identical. From this;box, we draw one chip at random, and record its value. We then put the chip;back in the box. We repeat this process two more times, making three draws in;all from this box.;14. How;many elements are in the sample space of this experiment?;15. What is the probability that the three numbers;drawn are all multiples of 5?;Questions 16 and 17 involve the random variablexwith probability;distribution given below.;Show all work. Just the answer;without supporting work, will receive no credit.;16.;Determine the expected value ofx.;17.;Determine the standard deviation ofx.;Consider the following situation for Questions 18, 19 and 20.Show all work. Just the answer, without supporting work, will receive no;credit.;Mimi just started her tennis;class three weeks ago. On average, she is able to return 15% of her opponent?s;serves. Let random number X be the number of serves Mimi returns. As we know;the distribution of X is a binomial probability distribution. If her opponent;serves 10 times, please answer the following questions;18. What is the number of trials (n), probability;of successes (p) and probability of failures (q), respectively?;19. Find the probability that she returns at most;8 of the 10 serves from her opponent.;20.;Find the mean and standard deviation for the probability distribution.;Refer to the following information for Questions 21, 22, and 23.Show all work. Just the answer, without supporting work, will receive no;credit.;The heights of pecan trees are normally distributed with a mean of 10 feet;and a standard deviation of 2 feet.;21.What is the probability that;a randomly selected pecan is between 8 and 12 feet tall?;22.Find the 80thpercentile;of the pecan tree height distribution.;23. If a random sample of 64 pecan trees is;selected, what is the standard deviation of the sample;mean?;24.A random sample of 625 SAT;scores has a mean of 1500. Assume that SAT scores have a population standard;deviation of 250. Construct a 95% confidence interval estimate of the mean SAT;scores.Show all work. Just the answer, without supporting;work, will receive no credit.;For a 95%;confidence interval, use z = 1.96.;In;interval notation, the 95% confidence interval is (1480.4, 1519.6).;What is the sample size for the conference;interval?;What is the point estimate for the;conference interval? ____\;The;appropriate distribution for calculating the confidence Interval is;What is the numerical value of the variable from the;appropriate distribution?;The;lower and upper limits for the 95% confidence interval are;25.;Given a sample size of 81, with sample mean 730 and sample standard deviation 90;we?perform;the following hypothesis test at the 0.05 level.H0:? = 750?H1:?;< 750;(a);Determine the test statistic.Show all work, writing the correct test statistic;without supporting work, will receive no credit.;(b);Determine the critical value.Show all work, writing the correct critical value;without supporting work, will;(c) What is your conclusion of the test? Please explain..;What is the appropriate distribution for performing;this Hypothesis test?;Determine the test statistic. ____-;Determine the critical value of the test statistic?;What is your conclusion for this hypothesis test?;26. Consider the hypothesis test given byH0:? = 530,?H1:??;530.?In a random sample of 225 subjects, the sample mean is found to be 525. Also, the?population standard deviation is 25.;(a);Determine the test statistic.Show all work, writing the correct test statistic;without supporting work, will receive no credit.;(b);Determine theP-value for this test.Show;all work, writing the correct P-value, without supporting work, will receive no;credit.;(c);Is there sufficient evidence to justify the rejection ofH0at the 0.01 level? Explain.;Since;the p-value of 0.0027 is less than the value of, the decision is to reject the null;hypothesis.;There is;sufficient evidence to justify the rejection of H0.;Determine the test statistic.;Determine the P-value for this test?;Is there sufficient evidence to justify the rejection;of Ho at?= 0.01 level?;27. A;certain researcher thinks that the proportion of women who say that the earth;is getting warmer is greater than the proportion of men. The research conducted;a survey, and found the following result:?In a random sample of 250;women, 70% said that the earth is getting warmer. In a random sample of 200;men, 67% said that the earth is getting warmer.?Assume we want to use a 0.05;significance level to test the claim.;(a);Identify the null hypothesis and the alternative hypothesis.;(b);Determine the test statistic.Show all work, writing the correct test statistic;without?supporting work, will;receive no credit.;(c);Determine the critical value.Show all work, writing the correct critical value,?without supporting work, will receive no;credit.;(d);Is there sufficient evidence to support the claim that the proportion of;women saying the earth is getting warmer is higher than the proportion of men;saying the earth is getting warmer? Justify your conclusion.;Identify the Null Hypothesis?;Identify the Alternate Hypothesis?;Determine the test statistic?;Determine the critical value?;Is there sufficient evidence to support the claim that;the proportion of women saying the earth is getting warmer is higher than the;proportion of men saying the earth is getting warmer?;Refer to the following data for Questions 28 and 29.;x;0;-1;1;2;4;y;3;-2;4;6;8;28. Find;an equation of the least squares regression line.Show all work, writing the correct equation, without;supporting work, will receive no credit.;29. Based;on the equation from # 28, what is the predicted value ofyifx= 3?Show all work and justify your answer.;30.;The UMUC Daily News reported that the color distribution for plain M&M?s;was: 35% brown, 20% yellow, 20% orange, 15% green, and 10% tan.Each piece of candy in a;random sample of 100 plain M&M?s was classified according to color,and the results are listed;below.;Color;Brown;Yellow;Orange;Green;Tan;Number;42;21;15;9;13;Assume we want to use a 0.10;significance level to test the claim that the published color distribution is;correct.;(a) Identify the null;hypothesis and the alternative hypothesis.?;(b) Determine the test;statistic.Show all work, writing the correct test statistic;without?supporting work, will receive no credit.?;The;value of the test statistic is calculated from;test statistic is X2 = 6.00.;(c) Determine the critical;value.Show all work, writing the correct critical value,?without supporting work, will receive no credit.?;(d) Is there sufficient;evidence to support the claim that the published color distribution is correct?;Justify your answer.;a

Paper#62116 | Written in 18-Jul-2015

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