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##### STAT200 Introduction to Statistics Final Examination

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solution

**Question**

Question;Refer to the following frequency distribution for;Questions 1, 2, 3, and 4.;The frequency distribution below shows the;distribution for checkout time (in minutes) in UMUC MiniMart between 3:00 PM;and 4:00 PM on a Friday afternoon.;Checkout Time (in minutes);Frequency;1.0 ? 1.9;5;2.0 - 2.9;3;3.0 ? 3.9;7;4.0 ? 4.9;3;5.0 ? 5.9;2;1.;What percentage of the checkout;times was less than 4 minutes? (5 pts)1.;Calculate the mean of this frequency;distribution. (10 pts)31.;In what class interval must the;median lie? (You don?t have to find the median) (5 pts);4. Assume that the smallest observation in this;dataset is 1.2 minutes. Suppose this;observation were;incorrectly recorded as.2 instead of 1.2;minutes. (5 pts) Will the mean increase, decrease, or remain;the same? Will the median increase, decrease or remain;the same?Refer to the following information for Questions 5 and;6;A 6-faced die is rolled two times. Let A be the event that the outcome of the;first roll is even. Let B be the event;that the outcome of the second roll is greater than 4.;5. What is;the probability that the outcomes of the second roll is greater than 4, given;that the first roll;is an even number? (10 pts) 6. Are A and;B independent? (5 pts)Refer to the following data to answer questions 7 and;8.;A random sample of Stat 200 weekly study times in;hours is as follows;4, 14, 15, 17, 20;7. Find the standard deviation. (10 pts)8. Are any of;these study times considered unusual in the sense of our textbook? (2.5 pts) Does this differ with your intuition? (2.5;pts)Refer to the following situation for Questions 9, 10;and 11.;The five-number summary below shows the grade;distribution of two STAT 200 quizzes.;Minimum;Q1;Median;Q3;Maximum;Quiz 1;12;40;60;95;100;Quiz 2;20;35;50;90;100;For each question, give your answer as one of the;following: (a) Quiz 1, (b) Quiz 2, (c) Both quizzes have the same value requested;(d) It is impossible to tell using only the given information. (5 pts each);9. Which quiz;has less interquartile range in grade distribution?10. Which quiz;has the greater percentage of students with grades 90 and over?;11. Which quiz;has a greater percentage of students with grades less than 60?12. What is;the probability that a randomly selected senior is in at least one of the two;classes?;(10 pts)13. If the;student is in the Calculus class, what is the probability the student is also;in the Statistics class?;(10 pts)14. A random;sample of 225 SAT scores has a mean of 1500. Assume that SAT scores have a;population;standard deviation of 300.;Construct a 95% confidence interval estimate of the mean SAT scores.;(15 pts)Refer to the following information for Questions 15;16, and 17.;A box contains 5 chips. The chips are numbered 1 through 5. 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.;15. How many;elements are in the sample space of this experiment? (5 pts)16. What is the;probability that the three numbers drawn are all different? (10 pts)17. What is;the probability that the three numbers drawn are all odd numbers? (10 pts)Questions 18;and 19 involve the random variable x with probability distribution given below.;X;2;3;4;5;6;P(x);0.1;0.2;0.4;0.1;0.2;18. Determine;the expected value of x. (10 pts)19. Determine;the standard deviation of x. (10 pts)Consider the following situation for Questions 20 and;21.;Mimi just started her tennis class three weeks;ago. On Average, she is able to return 15%;of her opponent?s serves. If her;opponent serves 10 times, please answer the following questions.;20. Find the;probability that she returns at most 2 of the 10 serves from her opponent. (10;pts)21. How many serves is she expected to return? (5;pts)22. Given a sample size of 64, with sample mean 730;and sample standard deviation 80, we perform;the following;hypothesis test. (20 pts);Ho? = 750;H1? < 750;What is the appropriate distribution;for performing this Hypothesis test?;Z distribution, t;distribution, Chi Square distribution, Empirical Rule;What is the critical value of the test statistic at?=;0.05 level?What is the P-value for this Hypothesis Test?What is your conclusion (decision) for;this hypothesis test at?= 0.05 level?Refer to the following information for Questions 23;24, and 25.;The heights of pecan trees are normally distributed;with a mean of 10 feet and a standard deviation of 2 feet.;23. What is;the probability that a randomly selected pecan tree is between 10 and 12 feet;tall? (10 pts)24. Find the 3rd quartile of the pecan;tree distribution. (5 pts);25. If a random sample of 100 pecan trees is;selected, what is the standard deviation of the sample mean? (5 pts)26. Consider;the hypothesis test given by;Ho;? = 530;H1;?? 530;In a random sample of 81 subjects, the sample mean is;found to be 524. Also, the population;standard deviation is?= 27. (20 pts);Calculate the Test Statistic.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. (25 pts);In a;random sample of 250 women, 70% said that the earth is getting warmer.;In a;random sample of 220 men, 68.18% said that the earth is getting warmer.;At the;.05 significance level, 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?;What is the Null Hypothesis?;28. Find an;equation of the least squares regression line. (15 pts);Complete the;following table;x;y;x^2;xy;y^2;0;4;0;0;16;-1;-2;1;2;4;1;5;1;5;25;2;6;4;12;36;3;8;9;24;64;5;21;15;43;145;What is the Y intercept of the;equation?;29 Using;the equation you calculated in question 28 What is the predicted value of y if;x=4? (10 pts)30. The UMUC;Daily News reported that the color distribution for plain M&M?s was: 40%;brown, 20% yellow, 20% orange;10% 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. Use a 0.05 significance level to test the claim that the;published color distribution is correct. (25 pts);Color;Brown;Yellow;Orange;Green;Tan;Number;45;13;17;7;18;What is the Null Hypothesis?What is the degrees of freedom for;this Hypothesis test?What is the numerical Chi Square;critical value?What is the numerical value of the;Chi Square test statistic?;31. Please note: Each time you re-due the Final Exam the;answer to question 31 may change, but the subject matter and format will not;change.

Paper#62431 | Written in 18-Jul-2015

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