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##### STATS Homework Week 8 Assignment

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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.;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;2.0 - 2.9;3.0 - 3.9;4.0 - 4.9;5.0 - 5.9;Total;7. Assume that the smallest observation in this;dataset is 1.2 minutes. Suppose thisobservation 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. LetAbe the event that the outcome of the first roll is greater;than 4. LetBbe 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.;x;1;2;3;4;5;P(x);0.1;0.2;0.3;0.1;0.3;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.;The 80th;percentile corresponds to a z-value of 0.8416.;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.;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;receive no credit.;(c) What;is your conclusion of the test? Please explain.;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.;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.;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.;Complete the following table;x;y;x^2;xy;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.;(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.

Paper#62240 | Written in 18-Jul-2015

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