# SOC 2805 Study Guide - Fall 2019, Comprehensive Final Exam Notes - Financial Statement, Variance, Triangulation

by OC1108230

Department

SociologyCourse Code

SOC 2805Professor

Karen A.BradleyStudy Guide

FinalThis

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Sample Problems for Exam 1: Fall 2016

1. An industrial sewing machine uses ball bearings that are targeted to have a diameter of 0.75

inch. The lower and upper specification limits under which the ball bearing can operate are 0.74 inch

(lower) and 0.76 inch (upper). Past experience has indicated that the actual diameter of the ball bearings

is approximately normally distributed, with a mean of 0.753 inch and a standard deviation of 0.004 inch.

You select a simple random sample with replacement of 25 ball bearings.

a. What is the mean of the sampling distribution?

0.753

b. What is the standard error of the sampling distribution?

0.00008

c. What is the probability that the sample mean is:

1. between the target and the population mean of 0.753?

P(0.75<X>0.753) = 0.499911583

2. between the lower specification limit and the target?

P(0.74<X>0.75) = 0.0000884173

3. greater than the upper specification limit?

P(X>0.76) = 0.999911583

4. less than the lower specification limit?

P(X<0.74) = Z = -16.23

d. The probability is 95% that the sample mean will be between which two values symmetrically

distributed around the mean?

.753-1.96(0.00008) = 0.7514; .753+1.96(0.00008) = 0.7546

1.96 = 95% C.I.

2. The fill amount of bottles of a soft drink is normally distributed, with a mean of 2.0 liters and a

standard deviation of 0.05 liter. If you select a random sample of 25 bottles, what is the probability that

the sample mean will be

a. between 1.99 and 2.0 liters?

P(1.99<X>2.0) = 0.079259709

b. below 1.98 liters?

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Sample Problems for Exam 1: Fall 2016

P(X<1.98) = 0.344578258

c. greater than 2.01 liters?

P(X>2.01) = 0.420740291

d. The probability is 99% that the sample mean amount of soft drink will be at least how much?

1.9742

e. The probability is 99% that the sample mean amount of soft drink will be between which two

values (symmetrically distributed around the mean)?

2-2.576(0.01) =1.9742 ; 2+2.576(0.01) = 2.0258

3. The branch manager of an outlet of a nationwide chain of pet supply stores wants to study

characteristics of her customers. In particular, she decides to focus on the amount of money spent by

customers. The results from a sample of 70 customers are as follows:

• Amount of money spent: 𝑋

̅ = $ 21.34, S = $ 9.22.

a. Construct a 95% confidence interval estimate of the population mean amount spent in the

pet supply store.

a. 19.1801; 23.4999

b. What assumptions, if any, are needed to construct this confidence interval? If one is

required, is the assumption valid? Justify your answer.

a. Normal distribution

4. A manufacturing company produces steel housings for electrical equipment. The main

component part of the housing is a steel trough that is made out of a 14- gauge steel coil. It is produced

using a 250- ton progressive punch press with a wipe- down operation that puts two 90- degree forms in

the flat steel to make the trough. The distance from one side of the form to the other is critical because

of weatherproofing in outdoor applications. The widths (in inches) are stored in the file Trough.

a. Construct a 99% confidence interval estimate of the mean width of the troughs.

8.4039; 8.4379

b. What assumptions, if any, are needed to construct this confidence interval? If one is

required, is the assumption valid? Justify your answer.

Normal Distribution

5. The owner of a gasoline station wants to study gasoline purchasing habits by motorists at his

station. He selects a random sample of 60 motorists during a certain week, with the following results:

• The amount purchased was gallons, 𝑋

̅=11.3 S = 3.1 gallons.

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