ENTC320 Exam 1 - KEY

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Print Name _______________________________

Carefully read the following before beginning.

1. This exam is closed book and closed notes.

2. Show your work, including the formulas you use.

3. Use the backside of the sheet if needed for your calculations.

4. Label all backside calculations with the problem number.

5. REMEMBER! Neatness and organization of your calculations count! The better you communicate what you did, the easier it is for me to determine if you know the material.

6. Formulas you may need are provided in a separate handout.

7. If you have any questions, ask them.

By initialing below, I confirm that I have read the above instructions and understand them. All questions I have about these instructions have been asked and have been answered to my satisfaction.

Initial here __________ On my honor, as an Aggie, I have neither given nor received unauthorized aid on this academic work. Signature ____________________________________________

ENTC320 Exam 1

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1. (20 points) Identify the most likely distribution of the data for each of these situations. Use the following symbols as answers.

B Binomial distribution BT Bernoulli trial N Normal distribution P Poisson distribution t t-distribution O Some other distribution

A. Number of scratches on oven doors __P__

B. Inside diameter of a bearing where is known __N__ C. Fraction non-conforming of memory modules __B__

D. Grade result for a single student in a pass/fail class __BT_

E. Heights of 25 elementary students __t__

F. Number of flaws per square inch on polished brass plates __P__

G. Number of customers arriving at a checkout station __P__

H. Percent yield of quad core CPUs __B__

I. Average diameter of 50 motor shafts __N__

J. Result of a functional test on one unit of product __BT_

ENTC320 Exam 1

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2. (20 points) What is the cumulative probability for each of the following Z-values?

Z = + 2.576 = ___0.995______ (0.99492, 0.99506) Z = 2.120 = ___1 0.98300 = 0.01700 Z = + 1.645 = ___0.95000____ (0.94950, 0.95053) Z = 3.090 = ___1 0.99900 = 0.00100 Z = + 1.282 = ___0.90000____ (0.89973, 0.90147)

What is the t-value for each of the following cases?

= 0.001 and n = 20 t = __3.579_______ = 0.025 and n = 120 t = __1.980_______ (2.000, 1.980) = 0.050 and n = 80 t = __1.664_______ (1.658, 1.671) = 0.100 and n = 29 t = __1.313_______ = 0.400 and n = 40 t = __0.255_______ (0.256, 0.255)

ENTC320 Exam 1

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3. (20 points) A manufacturer wants to know if the mean tensile strength of a cloth fiber is greater than 125 psi. Previous experience indicates that the standard deviation of tensile strength is 2 psi. A random sample of 8 fiber specimens has an average tensile strength of 127 psi. Technical problem: Does the mean tensile strength of this fiber exceed 125 psi? Use = 0.05. Statistical problem: Test H0: = 125 vs. H1: > 125. Statistical solution: Since the population standard deviation is known, use the Normal distribution to model these data. What is the value of Z? From the Standard Normal Table, Z = Z0.05 = 1.645 What is the value of Z0?

0

0127 125 2.8282 8

xZn

= = =

Since Z0 = 2.828 > Z = 1.645, therefore reject Ho.

Or, p-value(Z = 2.828) = 1 0.99767 = 0.00233 < = 0.05 Technical solution:

The mean tensile strength of the cloth fiber exceeds 125 psi with 95% confidence.

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4. (20 points) You are preparing to build a bookshelf for your room and need to purchase lumber suitable for this task. Your analysis of the maximum load requirement tells you that any board you select should have a mean strength greater than 2 lb/in2. Since the local hardware store doesnt have any specs on the strength of its wood types, you choose S4S aspen and test a random sample of ten specimens. This sample has an average strength of 2.31 lb/in2 and a standard deviation of 0.75 lb/in2. Since you have good medical insurance and good reflexes (in case the shelf breaks when you are near it), you choose = 0.10 for your acceptable risk. Technical problem: Is the mean strength of the chosen aspen greater than 2 lb/in2?

Statistical problem: Test H0: = 2.0 vs. H1: > 2.0 Statistical solution: Since we do not know the population standard deviation and the sample size is 10, we must use the t-distribution to model these data. t, n1 = t0.10, 101 = 1.383

307.110/75.00.231.2

/0===

nSxt

Since t0 = 1.307 < t0.05,9 = 1.383, therefore do not reject H0. Technical solution: The mean tensile strength of the chosen aspen is not greater than 2.0 lb/in2 with 90% confidence.

ENTC320 Exam 1

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5. (10 points) These questions apply to problem 3. A. What is the p-value for Z0? p = 1 0.99766 = 0.00234 (0.99760, 0.99767) B. What is a 95% confidence interval about the mean value of fiber tensile strength?

nZx

nZx 2/2/ +

127 1.96(2/8) 127 + 1.96(2/8) 125.61 128.61 6. (10 points) These questions apply to problem 4. A. What is the p-value for t0? p = 0.117 (0.0112) (0.25, 0.10) B. What is a 90% confidence interval about the mean value of board strength?

nstx

nstx 2/2/ +

2.31 1.833(0.75/10) 2.31 + 1.833(0.75/10) 1.88 2.74