PROBLEM SOLVING: Solve the following problems. Show all pertinent solutions.

1.A car battery dealer is trying to determine which of the brands of car battery he is selling has a longer life span. He conducted an investigation by interview his customers and was able to get the following results: Brand X Brand Y Mean life span 4.5 years 4.9 years Standard deviation 0.56 year 0.45 year Sample size 10 12

If you were the car dealer, could you conclude that brand Y is superior to Brand X? Use 5% level of significance.

2.A die was rolled 210 times. The results are shown below.

Based on the data, can we say that teaching efficiency is related to educational background? Use 5% level of significance.

5.The average typing speed of a good typist is said to be 60 words per minute. In a certain company, 45 applicants were given a typing test and the results showed a mean of 55 words per minute with a standard deviation of 10 minutes. Based on these results, can we say that the typing speed of the 45 applicants is below the average? Use α = 0.03.

6.A lot contains 20 electric bulbs, 5 of which are defective. In how many ways can 4 bulbs be taken for inspection such that: (a) no defective electric bulb is included? (b) 2 of the defective bulbs...

...1. Indicate whether each of the following is a constant or a variable (5 points)
a. Resting pulse rate – Variable
b. Number of bits in a terabyte – Constant
c. Peso equivalent to a Swiss Franc – Variable
d. Number of inches in a mile – Constant
e. Number of neutrons in a carbon atom – Constant
2. Indicate whether the following variables are quantitative or qualitative and specify the scale of measurement. (10 points)
a. Admitting diagnosis of patients to a mental hospital – Qualitative, Nominal Scale
b. Underarm temperature of day-old infants born in a hospital – Quantitative (Continuous), Interval Scale
c. Viral DNA load (copies/ml) – Quantitative (Discrete), Ratio Scale
d. Body Mass Index – Quantitative (Continuous), Ratio Scale
e. Age at diagnosis of breast cancer – Quantitative (Discrete), Interval Scale
3. Multiple Choice (2 points). A nominal scale is used for: A
a. All categorical data
b. Discrete data with categories that do not follow a natural sequence
c. Continuous data that follow a natural sequence
d. Discrete data with categories that follow a natural sequence
e. Quantitative data
4. A study of 275 patients admitted to a hospital during the past year revealed that, on the average, the patients lived 15 miles from the hospital (6 points)
a. What is the variable of interest?
The variable of interest include the distance of a patient’s...

...More
19
Confidence
Interval
Problem
Answers
AP Statistics Quiz A – Chapter
– Key
A statistics professor asked her students whether or not they were registered to vote. In a sample of
50 of her students (randomly sampled from her 700 students), 35 said they were registered to vote.
1. Find a 95% confidence interval for the true proportion of the professor’s students who were
registered to vote. (Make sure to check any necessary conditions and to state a conclusion in
the context of the problem.)
We have a random sample of less than 10% of the professor’s students, with 35 expected successes
(registered) and 15 expected failures (not registered), so a Normal model applies.
n
50, pˆ
35
50
0.70, qˆ 1 pˆ
Our 95% confidence interval is:
pˆ r z
SE pˆ 0.70 r 1.96 0.065
0.30 , so SE pˆ
0.70 r 0.127
ˆˆ
pq
n
0.700.30
50
0.065
0.573 to 0.827
We are 95% confident that between 57.3% and 82.7% of the professor’s students are registered to vote.
2. Explain what 95% confidence means in this context.
If many random samples were taken, 95% of the confidence intervals produced would contain the actual
percentage of the professor’s students who are registered to vote.
3. What is the probability that the true proportion of the professor’s students who were registered
to vote is in your confidence interval?
There is no probability involved—once the interval is constructed, the true...

...Trajico, Maria Liticia D.
BSEd III-A2
REFLECTION
The first thing that puffs in my mind when I heard the word STATISTIC is that it was a very hard subject because it is another branch of mathematics that will make my head or brain bleed of thinking of how I will handle it. I have learned that statistic is a branch of mathematics concerned with the study of information that is expressed in numbers, for example information about the number of times something happens. As I examined on what the statement says, the phrase “number of times something happens” really caught my attention because my subconscious says “here we go again the non-stop solving, analyzing of problems” and I was right. This course of basic statistic has provided me with the analytical skills to crunch numerical data and to make inference from it. At first I thought that I will be alright all along with this subject but it seems that just some part of it maybe it is because I don’t pay much of my attention to it but I have learned many things. I have learned my lesson.
During our every session in this subject before having our midterm examination I really had hard and bad times in coping up with this subject. When we have our very first quiz I thought that I would fail it but it did not happen but after that, my next quizzes I have taken I failed. I was always feeling down when in every quiz I failed because even though I don’t...

...Me1
ProblemSet #2
The US College Enrollment and the “Third Law of Demand”
A theorem proposed by Professors Alchian and Allen in their text, University Economics (1964) has had several rebirths of interest in the literature. The so-called “third law of demand,” or “relative price theorem,” holds that a fixed cost added to a good of varying quality causes the consumer to prefer the category considered of higher quality to the lower.
Recently a number of studies, keeping this theorem in mind have looked into a relationship between the ratio of public to private enrollment and unemployment in cross-sectional as well as in time series data. Part of the full cost of participating in higher education is foregone employment income. In their regression model, these studies have regressed the public/private ENROLLMENT RATIO (as an indicator of relevant demand) against UNEMPLOYMENT RATES (as an indicator of cost) as well as a number of variables designed to account for “other things” which tend to vary at the same time, such as income, financial aid and tuition ratios. Tuition ratio is typically specified as the ratio of the full cost (including forgone employment income) of public higher education (Pa) to private higher education (Pb), where Pa is less than Pb.
In Table 1, below, a cross-sectional model reveals the relationships between relative education demands by public and private university students (as measured by state level ENROLLMENT...

...Yue
Office: KRAN B024A
Office Hours: Monday 12 noon-1 pm &Tuesday 9-10 am.
Phone: 496-1458 email: kyue@purdue.edu
Course goal: We provide a broad overview of the microeconomic aspects of the international economy. We emphasize the development of analytical tools. We also show how we can apply these tools to questions with real-world relevance.
Prerequisites:
Econ 251, Econ 252 (Principles of Microeconomics, Principles of Macroeconomics)
Textbook:
1. Feenstra and Taylor, “International Trade”, 2nd Edition. We follow the textbook very closely in class and cover about 70% of its contents.
2. Yeaple, Study Guide for Feenstra and Taylor’s International Trade, 2nd Edition. We take many practice problems from the Study Guide.
5 copies of the textbook (2nd edition) and 5 copies of the Study Guide (2nd edition) are on reserve at Parrish (the management-and-econ library).
Distribution of homework and other materials:
Katalyst - https://webapps.krannert.purdue.edu/kap/
Course Grades:
Quizzes (best 5 out of 6) 30%
Homework Assignments (best 3 of 4) 25%
Extra Credit Questions 10%
Midterm (in class) 20%
Final Exam 25%
Dates for Quizzes, Homework Assignments, Review Sessions and Exams:
These dates are fixed and will not change. See the class calendar.
Course Materials:
This should be regarded as a likely (but not 100%-certain) schedule as some topics may run shorter or longer than...

...EC 109
Autumn 2011
Dr. Mani
ProblemSet 2
Due Date: Oct31, Monday – between 9 & 11 AM in room S 2.132
Please keep a copy of your assignment and show all your work clearly.
(1) Mr. J. Bond, a retired movie actor, consumes only grapes and the composite good Y (i.e. price of Y is £1). His income consists of £10000 a year from his investment fund plus the proceeds of whatever he sells of the 2000 bushels of grapes he harvests annually from his vineyard in Tuscany. Last year, grapes sold at £2 per bushel and Bond consumed all 2000 bushels of his grapes, in addition to 10,000 units of Y. This year, the price of grapes is £3 per bushel (and the price of the composite good Y is the same as before). If Bond has well-behaved preferences, will his consumption of grapes this year be greater than, less than or the same as last year’s? How about his consumption of the composite good? (Hint: Graph both years’ budget constraints and think about whether last year’s bundle is affordable to Mr. R).
(2) Suppose Carmela’s income is £100 per week, which she allocates between sandwiches and books. Sandwiches cost £2 each. Books cost £10 each if she purchases between 1 and 5 books. If she purchases more than 5 books in a week, the price falls to £5 for the 6th book and all subsequent books. Draw the budget constraint. Is it possible that Carmela might have more than...

...Energy
1. A man climbs on to a wall that is 5 m high and gains 2200 J of potential energy. What is the mass of the man?
Given: Formula:
h = 5 m m = PE/gh
PE = 2200 J
Solution:
m = 2200 J / (9.8 m/s2 x 5 m)
m = 49 kg
2. Calculate the kinetic energy of a 500 kg car travelling at 50 m/s.
Given: Formula:
m = 500 kg KE = mv2/2
v = 50 m/s
Solution:
KE = 500 kg x (50 m/s)2 / 2
KE = 625 000 J
Power
3. Riley climbs a flight of stairs in 3 minutes. If he weighs 700 N and the stairs is 20 m from the ground, how much power will she develop?
Given: Formula:
t = 3 mins = 180 s P = Wd/t
W = 700 N
d = 20 m
Solution:
P = 700 N x 20 m / 180 s
P = 77.8 J/s
4. How much power is developed by a car that runs 80 m/s when the force is equal to 50 000 N.
Given: Formula:
V = 80 m/s W = Fv
F = 50 000 N
Solution:
W = 50 000 N x 80 m/s
W = 4 000 000 J/s
Electricity
5. Charges of 6 and + 4 nC are 3 m apart. Determine the force they exert on each other, and the electric field at a point midway between them.
Given: Formula:
k = 9 x 109 Felec = k q1 q2 /r2
q1 = 6 x 109 C
q2 = 4 x 109 C
r = 3 m
Felec = (9 x 109)(6 x 109)(4 x 109)/32
Felec = 24 x 109 N
6. A 50 cm piece of nichrome wire is used in a home heating element. The cross sectional area of the wire is 0.05 mm2. What is the resistance of the heating element? If it is operated on household current (110 V),...

...BE 13.8
Vertical analysis (common-size) percentages for Vallejo Company’s sales, cost of goods sold, and expenses are listed below:
VERTICAL ANALYSIS 2012 2011 2010
Sales 100.0% 100.0% 100.0%
Cost of goods sold 60.5 62.9 64.8
Expenses 26.0 26.6 27.5
Net Income 13.5 10.5 7.7
Did Vallejo’s net income as a percent of sales increase, decrease, or remain unchanged over the 3 year period. Provide numerical support for your answer.
Sales – Cost of Goods Sold – Expenses = Net Income
100 – 64.8 – 27.5 = 7.7 for 2010
100 – 62.9 – 26.6 = 10.5 for 2011
100 – 60.5 – 26.0 = 13.5 for 2012
During the 3 year period of 2010-2012, the net income increased as a percent of sales for the Vallejo Company due to the decrease as a percent of sales in both the cost of goods sold and expenses every year.
BE 13.9
Horizontal analysis (trend-analysis) percentages for Spartan Company’s sales, cost of goods sold, and expenses are listed below:
VERTICAL ANALYSIS 2012 2011 2010
Sales 96.2% 104.8% 100.0%
Cost of goods sold 101.0 98.0 100
Expenses 105.6 95.4 100
Net Income (110.4) (88.6) 0
Explain whether Spartan’s net income as a percent of sales increase, decrease, or remain unchanged over the 3 year period.
Sales – Cost of Goods Sold – Expenses = Net Income
100 – 100 – 100 = 0.0 for 2010
104.8 – 98.0– 95.4 = -88.6 for 2011
96.2 – 101.0 – 105.6 = -110.4 for 2012
In 2010, the net income for the Spartan Company is 0. In 2011, the company’s net income decreased as a percent of...