Posted: July 20th, 2023

STAT 200: Introduction to Statistics Final Examination,

STAT 200: Introduction to StatisticsFinal Examination, Spring 2016 OL4Page 1 of 45.A box contains 3 marbles, 1 red, 1 green, and 1 blue. Consider an experiment that consists oftaking 1 marble from the box, then replacing it in the box and drawing a second marble fromthe box. (Show all work. Just the answer, without supporting work, will receive no credit.)(a)(b)List all outcomes in the sample space.What is the probability that neither marble is red?fraction form)6.There are 1000 students in a high school. Among the 1000 students, 250 students take APStatistics, and 300 students take AP French. 100 students take both AP courses. Let S be theevent that a randomly selected student takes AP Statistics, and F be the event that a randomlyselected student takes AP French. Show all work. Just the answer, without supporting work,will receive no credit.(a)(b)Provide a written description of the complement event of (S OR F).7.Consider rolling two fair dice. Let A be the event that the sum of the two dice is 8, and B be theevent that the first one lands on 6.(a)What is the probability that the first one lands on 6 given that the sum of the two dice is 8?Show all work. Just the answer, without supporting work, will receive no credit.Are event A and event B independent? Explain.(Express the answer in simplestWhat is the probability of complement event of (S OR F)?(b)9.Assume random variable x follows a probability distribution shown in the table below.Determine the mean and standard deviation of x. Show all work. Just the answer, withoutsupporting work, will receive no credit.xP(x)-20.100.210.330.150.310.Mimi plans on growing tomatoes in her garden. She has 15 cherry tomato seeds. Based on herexperience, the probability of a seed turning into a seedling is 0.40.(a)Let X be the number of seedlings that Mimi gets. As we know, the distribution of X is abinomial probability distribution. What is the number of trials (n), probability of successes (p)and probability of failures (q), respectively?STAT 200: Introduction to StatisticsFinal Examination, Spring 2016 OL4Page 2 of 4(b)Find the probability that she gets at least 2 cherry tomato seedlings. (round the answer to 3decimal places) Show all work. Just the answer, without supporting work, will receive no credit.11.Assume the weights of men are normally distributed with a mean of 172 lbs and a standarddeviation of 30 lbs. Show all work. Just the answer, without supporting work, will receive nocredit.(a)Find the 90th percentile for the distribution of men’s weights.(b)What is the probability that a randomly selected man weighs more than 185 lbs?12.Assume the IQ scores of adults are normally distributed with a mean of 100 and a standard deviationof 15. Show all work. Just the answer, without supporting work, will receive no credit.(a)(b)If a random sample of 25 adults is selected, what is the standard deviation of the sample mean?What is the probability that 25 randomly selected adults will have a mean IQ score that isbetween 95 and 105?13.A survey showed that 80% of the 1600 adult respondents believe in global warming. Construct a95% confidence interval estimate of the proportion of adults believing in global warming. Showall work. Just the answer, without supporting work, will receive no credit.14.In a study designed to test the effectiveness of acupuncture for treating migraine, 100 patients wererandomly selected and treated with acupuncture. After one-month treatment, the number ofmigraine attacks for the group had a mean of 2 and standard deviation of 1.5. Construct a 95%confidence interval estimate of the mean number of migraine attacks for people treated withacupuncture. Show all work. Just the answer, without supporting work, will receive no credit.15.Mimi is interested in testing the claim that more than 75% of the adults believe in global warming.She conducted a survey on a random sample of 100 adults. The survey showed that 80 adults inthe sample believe in global warming.Assume Mimi wants to use a 0.05 significance level to test the claim.(a)(b)(c)(d)Identify the null hypothesis and the alternative hypothesis.Determine the test statistic. Show all work; writing the correct test statistic, without supportingwork, will receive no credit.Determine the P-value for this test. Show all work; writing the correct P-value, withoutsupporting work, will receive no credit.Is there sufficient evidence to support the claim that more than 75% of the adults believe inglobal warming? Explain.STAT 200: Introduction to Statistics16.Final Examination, Spring 2016 OL4Page 3 of 4In a study of memory recall, 5 people were given 10 minutes to memorize a list of 20 words.Each was asked to list as many of the words as he or she could remember both 1 hour and 24hours later. The result is shown in the following table.Number of Words RecalledSubject 1 hour later24 hours later114122181531194131251212Is there evidence to suggest that the mean number of words recalled after 1 hour exceeds themean recall after 24 hours?Assume we want to use a 0.10 significance level to test the claim.(a)(b)(c)(d)17.(a)(b)(c)(d)18.Identify the null hypothesis and the alternative hypothesis.Determine the test statistic. Show all work; writing the correct test statistic, without supportingwork, will receive no credit.Determine the P-value for this test. Show all work; writing the correct P-value, withoutsupporting work, will receive no credit.Is there sufficient evidence to support the claim that the mean number of words recalled after 1hour exceeds the mean recall after 24 hours? Justify your conclusion.In a pulse rate research, a simple random sample of 40 men results in a mean of 80 beats perminute, and a standard deviation of 11.3 beats per minute. Based on the sample results, theresearcher concludes that the pulse rates of men have a standard deviation greater than 10 beatsper minutes. Use a 0.05 significance level to test the researcher’s claim..Identify the null hypothesis and alternative hypothesis.Determine the test statistic. Show all work; writing the correct test statistic, withoutsupporting work, will receive no credit.Determine the P-value for this test. Show all work; writing the correct P-value, withoutsupporting work, will receive no credit.Is there sufficient evidence to support the researcher’s claim? Explain.The UMUC MiniMart sells four different types of teddy bears. The manager reports that thefour types are equally popular. Suppose that a sample of 500 purchases yields observed counts150, 120, 110, and 120 for types 1, 2, 3, and 4, respectively.STAT 200: Introduction to StatisticsTypeNumberFinal Examination, Spring 2016 OL4115021203110Page 4 of 44120Assume we want to use a 0.05 significance level to test the claim that the four types are equallypopular.(a)(b)Identify the null hypothesis and the alternative hypothesis.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, withoutsupporting work, will receive no credit.(d)Is there sufficient evidence to support the manager’s claim that the four types areequally popular? Justify your answer.20. A study of 10 different weight loss programs involved 500 subjects. Each of the 10 programs had50 subjects in it. The subjects were followed for 12 months. Weight change for each subject wasrecorded. Mimi wants to test the claim that the mean weight loss is the same for the 10 programs.(a)Complete the following ANOVA table with sum of squares, degrees of freedom, and meansquare (Show all work):Source ofVariationFactor(Between)Error (Within)Total(b)(c)(d)Sum of Squares(SS)Degrees ofFreedom (df)Mean Square(MS)42.361100.76N/ADetermine the test statistic. Show all work; writing the correct test statistic, without supportingwork, will receive no credit.Determine the P-value for this test. Show all work; writing the correct P-value, withoutsupporting work, will receive no credit.Is there sufficient evidence to support the claim that the mean weight loss is the same for the10 programs at the significance level of 0.05? Explain.

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