test3-fa22

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Texas Tech University *

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2301

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Mathematics

Date

Apr 3, 2024

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pdf

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6

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MATH 3342-022 Test 3 Fall 2022 Test 3 Key Name (Last, First): INSTRUCTIONS e This exam consists of two parts. Part I is comprised of 10 multiple-choice questions (no partial credit) and is worth 50 points. Part II consists of partial-credit-type questions and is worth 50 points. e Write the answer of your choice, A-E, to the Part I questions in the Answer: space provided. Use CAPITALS, e.g. B instead of b. e Give complete answers to the Part II questions in order to get maximum credit. Even if you do not know the answer try to write something down; remember that blank space equals zero points. e The following aids are allowed on this test: — A table of standard normal curve areas (Table A.3) and a table of critical values for the t-distribution (Table A.5). — A formula-sheet consisting of no more than 1 sheet (2 pages) of 8.5 x 11 paper. — A standard scientific calculator. Usage of a smartphone is permitted provided it is ONLY used as a scientific calculator (you may NOT use it as a communication device, to access the internet, stored text, etc.).
MATH 3342-022 Test 3 Fall 2022 PART 1 1. Which of the following statements is correct or appropriate (select one)? (a) The sample mean regarded as a random variable, is denoted by X, while the calculated value of the sample mean from data is denoted by . (b) The distribution of the sample mean X is sometimes called its sampling distribution. d ) (c) A statistic is any quantity that can be calculated from a sample of data. (d) All of the above are correct/appropriate *** ) (e) None of the above is correct/appropriate Answer: 2. Let X1,...,Xe4 be a random sample (IID) from a population with mean of p = 72 and a standard deviation of ¢ = 16. Then, the distribution of the sample mean X has a standard deviation of: (a) (b) (c) 8 (d) 1 ) (e) None of the above Answer: 3. In addition to predicting the standard deviation of X in Question 2, the Central Limit Theorem also predicts that: X is approximately normal with mean 72 *** X is exactly normal with mean 72 and variance 162 X is approximately gamma with o = 72/5 and 8 =5 he Central Limit Theorem does not apply here None of the above is accurate Answer: 4. A random sample (IID) of size 36 is drawn from a population with mean of 5 and standard deviation of 10. Let T be the sample total. Then, E(T) is: None of the above Answer: None of the above Answer:
MATH 3342-022 Test 3 Fall 2022 6. For quality control purposes, a manufacturer of bike helmets wants to determine the true proportion of defectives, p, in their manufacturing process. To this end, a random sample of 50 bike helmets is selected, and it is found that 11 of them are flawed. Based on these data, the best estimate of p would be: None of the above Answer: 7. Construct a 95% confidence interval for p in Question 6. (a) (0.105, 0.335) *** (b) (0.023, 0.197) (c) (0.361, 0.639) (d) (0.124, 0.316) ) (e) None of the above Answer: 8. A 99% confidence interval for the mean u of a normal population when the standard deviation o is known is found to be (98.6, 118.4). If the confidence level is reduced to 95%, the confidence interval for pu: (a) Becomes wider (b) Becomes narrower *** (c (d (e) None of the above Answer: ) ) ) Remains unchanged ) Can be constructed from the given information ) 9. In Question 8, what is the value of the sample mean x? Cannot be determined from the given information None of the above Answer: 10. In Question 8, what is the minimum sample size required for the 99% confidence interval for u to have a width of w = 10, if o = 127 None of the above Answer:
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