Math Assignment Questions

1. True or False. Justify for full credit. (25 pts)(a) If there is no linear correlation between two variables, then these two variables arenot related in any way.(b) If the variance from a data set is zero, then all the observations in this data set areidentical.(c)P(A and ) =1, where is the complement of A.(d) In a hypothesis testing, if the P-value is less than the significance level , we rejectthe null hypothesis.(e) The volume of milk in a jug of milk is 128 oz. The value 128 is from a discrete dataset.Refer to the following frequency distribution for Questions 2, 3, 4, and 5. Show all work. Just theanswer, without supporting work, will receive no credit.The frequency distribution below shows the distribution for checkout time (in minutes) inUMUC MiniMart between 3:00 and 4:00 PM on a Friday afternoon.Checkout Time (in minutes)Frequency1.0 – 1.922.0 – 2.9123.0 – 3.924.0 – 4.942. What percentage of the checkout times was less than 3 minutes? (5 pts)3. In what class interval must the median lie? Explain your answer. (5 pts)4. Calculate the mean of this frequency distribution. (5 pts)5. Calculate the standard deviation of this frequency distribution. (Round the answer to twodecimal places) (10 pts)Refer to the following data to answer questions 6, 7 and 8. 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:2 15 15 18 406. Find the sample standard deviation. (Round the answer to two decimal places) (10 pts)7. Find the coefficient of variation. (5 pts)8. Are any of these study times considered unusual based on the Range Rule of Thumb?Show work and explain. (5 pts)Refer to the following information for Questions 9, 10 and 11. Show all work. Just the answer,without supporting work, will receive no credit.Consider selecting one card at a time from a 52-card deck. Let event A be the first card is an ace,and event B be the second card is an ace. (Note: There are 4 aces in a deck of cards)9. If the card selection is without replacement, what is the probability that the first card is an ace andthe second card is also an ace? (Express the answer in simplest fraction form) (10 pts)10. If the card selection is with replacement, what is the probability that the first card is an ace andthe second card is also an ace? (Express the answer in simplest fraction form) (10 pts)11. Are A and B independent when the selection is with replacement? Why or why not? (5 pts)Refer to the following information for Questions 12 and 13. Show all work. Just the answer,without supporting work, will receive no credit.There are 1000 juniors in a college. Among the 1000 juniors, 200 students are takingSTAT200, and 100 students are taking PSYC300. There are 50 students taking bothcourses.12. What is the probability that a randomly selected junior is taking at least one of these twocourses? (10 pts)13. What is the probability that a randomly selected junior is taking PSYC300, given thathe/she is taking STAT200? (10 pts)14. UMUC Stat Club must appoint a president, a vice president, and a treasurer. There are 10qualified candidates. How many different ways can the officers be appointed? (5 pts)15. Mimi has seven books from the Statistics is Fun series. She plans on bringing three of the sevenbooks with her in a road trip. How many different ways can the three books be selected? (5 pts)Questions 16 and 17 involve the random variable x with probability distribution given below.Show all work. Just the answer, without supporting work, will receive no credit.x-1012P (x )0.10.30.40.216. Determine the expected value of x. (5 pts)17. Determine the standard deviation of x. (Round the answer to two decimal places) (10 pts)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 20% of heropponents serves. Assume her opponent serves 8 times.18. Let X be the number of returns that Mimi gets. As we know, the distribution of X is a binomialprobability distribution. What is the number of trials (n), probability of successes (p) andprobability of failures (q), respectively? (5 pts)19. Find the probability that that she returns at least 1 of the 8 serves from her opponent. (10 pts)20. How many serves can she expect to return? (5 pts)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 dogwood trees are normally distributed with a mean of 9 feet and a standard deviation of3 feet.21. What is the probability that a randomly selected dogwood tree is greater than 12 feet? (5 pts)22. Find the 75th percentile of the dogwood tree height distribution. (10 pts)23. If a random sample of 36 dogwood trees is selected, what is the probability that the mean heightof this sample is less than 10 feet? (10 pts)24. A random sample of 100 light bulbs has a mean lifetime of 3000 hours. Assume that thepopulation standard deviation of the lifetime is 500 hours. Construct a 95% confidence intervalestimate of the mean lifetime. Show all work. Just the answer, without supporting work, willreceive no credit. (15 pts)25. Given a sample size of 100, with sample mean 730 and sample standard deviation 100,we perform the following hypothesis test at theH0_u=750H1:u750(a) Determine the test statistic. Show all work; writing the correct test statistic, withoutsupporting work, will receive no credit.(b) Determine the critical values. 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. (20 pts)26. Consider the hypothesis test given byH0_p=0.5H1:p<0.5In a random sample of 225 subjects, the sample proportion is found to be p = 0.51.(a) Determine the test statistic. Show all work; writing the correct test statistic, withoutsupporting work, will receive no credit.(b) Determine the P-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 of H 0 at the a =0.01 level?Explain. (20 pts)27. In a study of memory recall, 5 people were given 10 minutes to memorize a list of 20words. Each was asked to list as many of the words as he or she could remember both 1hour and 24 hours later. The result is shown in the following table.Number of Words RecalledSubject1 hour later24 hours later114122181531194131251212Is there evidence to suggest that the mean number of words recalled after 1 hour exceedsthe mean recall after 24 hours?Assume we want to use a 0.01 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, withoutsupporting 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 mean number of wordsrecalled after 1 hour exceeds the mean recall after 24 hours? Justify your conclusion.(20 pts)Refer to the following data for Questions 28 and 29.x0-135y3-23828. Find an equation of the least squares regression line. Show all work; writing the correctequation, without supporting work, will receive no credit. (15 pts)29. Based on the equation from # 28, what is the predicted value of y if x = 4? Show all workand justify your answer. (5 pts)30. The UMUC MiniMart sells four different types of teddy bears. The manager reports thatthe four types are equally popular. Suppose that a sample of 100 purchases yieldsobserved counts 30, 24, 22, and 24 for types 1, 2, 3, and 4, respectively.Type1Number 30234242224Assume we want to use a 0.10 significance level to test the claim that the four types areequally popular.(a) Identify the null hypothesis and the alternative hypothesis.(b) Determine the test statistic. Show all work; writing the correct test statistic, withoutsupporting 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 managers claim that the four types areequally popular? Justify your answer. (20 pts)