STAT 190 Final Fall 2021

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Truman State University *

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190

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Statistics

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Jan 9, 2024

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2021 Fall STAT 190 Final 1.(10 points) Classify each of the following variables as qualitative (categor- ical) or quantitative: (1). Number of new automobiles sold at a dealership on a given day.(2 points) (2). Weight in carats of an uncut diamond.(2 points) (3). Brand name of pair of running shoes.(2 points) (4). Student ID number.(2 points) (5). Assessed value of a house.(2 points) 2.(13 points) ( Cough, cough: ) The following table presents the number of days a sample of patients repoted a cough lasting from an acute cough illness. 16 20 21 20 19 17 18 12 22 17 16 24 15 13 21 16 21 20 20 19 18 16 19 20 21 21 14 16 16 14 17 18 15 14 20 20 13 15 18 20 19 21 19 18 20 a. Construct a relative frequency distribution table.(5 classes and class width is 3)(5 points) b. Construct a relative frequency histogram.(3 points) c. Which shape best describes the following histogram?(2 points) (i) Skewed left (negatively skewed) (ii) Skewed right (positively skewed) (iii) Symmetric d. Which of the following is true about the value of the mean compared to the median for the given histogram?(2 points) (i) The mean is greater than the median. (ii) The mean is less than the median. (iii) The mean is equal to the median. e. Find the percentage of patients who cough at least 21 days.(1 points) 1
3.(11 points) High blood pressure: The National Health and Nutrition Survey reported that 30% of adults in the US have hypertension(high blood pressure). A sample of 25 adults is studied. Let X denote the number of adults who have hypertension in the sample. a. What is the mean number who have hypertension in a sample of 25 adults?(2 points) b. What is the probability that exactly 6 of them have hypertension?(3 points) c. What is the probability that fewer than 4 have hypertension?(3 points) d. Would it be unusual if more than 10 of them have hypertension?(3 points) 4.(11 points):Choose the correct statement for the following questions. Below are the waiting times in minutes for a random sample of 24 patients at an emergency room (Er). Note that the sample mean is 70 minutes and the sample standard deviation is 79.1806 minutes. 0 10 10 10 10 10 20 20 30 30 30 40 40 40 50 50 80 90 130 140 150 160 200 330 (1).The five number summary for these data is 0, 10, 40, 110, 330, and the inter-quartile range is 100 minutes. We interpret the IQR to mean that(3 points) a. 50% of the data values are below 100 minutes b. the spread of the middle 50% of the data values is 100 minutes c. values above 100 minutes are outliers d. values above 140 minutes are outliers 2
(2) We wish to construct the 95% confidence interval for the population mean waiting time at this ER. i. What assumptions are necessary to construct this confidence interval? Are those assumptions reasonable for these data? Briefly explain why or why not.(2 points) ii. Regardless of your answer above, suppose that the necessary assumptions are met. Note that the sample mean is 70 minutes, the sample standard de- viation is 80 minutes, and the population standard deviation is unknown. Then the 95% confidence interval for the population mean waiting time at this ER is given by (3 points) a. 70 plus-minus 26.32 b. 70 plus-minus 27.376 c. 70 plus-minus 31.36 d. 70 plus-minus 33.024 3) If we were to construct a 90% confidence interval for the same data, the 90% interval (3 points) a. would be narrower than the 95% interval. b. would be of the same width as the 95% interval. c. would be wider than the 95% interval. d. can not be determined from the given information. 5.(11 points) TV sets: A Nielsen Company report states that the mean number of TV sets in a U.S. household is 2.24. Assume the standard devia- tion is 1.2. A sample of 85 households is drown. Round all answers to four decimal places. a. What is the probability that the sample mean number of TV sets is greater than 2?(3 points) b. What is the probability that the sample mean number of TV sets is between 2.5 and 3?(4 points) c. Can you tell weather it would be unusual for an individual household to have fewer than 2 TV sets? Explain.(4 points) 3
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