sample of mid term exam

8/10/2019 Sample of Mid Term Exam

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Introduction to Statistical Methods

Sample of Midterm exam

Name:________________________________________________Student ID ___________________1. The American Association of Individual Investments informed about 94 secondary shares newly emitted (AAII

Journal, February 1997). The companies were between small and medium and did not quote in the main stock

markets. The following table shows information on where the shares were marketed New York Stock Exchange

(NYSE), the American Stock Exchange (AMEX) and Over the Counter (OTC) as well as the earnings for eachshare and the ratio price to earnings for 20 of those companies:

Share Market Earnings Ratio

Per Share price to

(Dollars) earnings

Chemi-Trol OTC 0.39 27.30

Candies OTC 0.07 36.20

TST/Impreso OTC 0.65 12.70

Unimed Pharm. OTC 0.12 59.30

Skyline Chili AMEX 0.34 19.30

Cyanotech OTC 0.22 29.30

Catalina Light. NYSE 0.15 33.20

DDL Elect. NYSE 0.10 10.20Euphonix OTC 0.09 49.70

Mesa Labs OTC 0.37 14.40

RCM Tech. OTC 0.47 18.60

Anuhco AMEX 0.70 11.40

Hello Direct OTC 0.23 21.10

Hilite Industres OTC 0.61 7.80

Alpha Tech OTC 0.11 34.60

Wegener Grup OTC 0.16 24.50

U.S. Home&Garden OTC 0.24 8.70

Chalone Wine OTC 0.27 44.40

ENG. Support Sys. OTC 0.89 16.70

Int. Remote Imaging AMEX 0.86 4.70

Construct the relative cumulative frequency distribution for the column ratio price to earnings, use the class limits

0.0 to 9.9, 10.0 to 19.9, etc. What is the cumulative relative frequency for the class 30 to 39.9?


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2. You are given the following data on the ages of employees at a company.

26 32 28 45 5852 44 36 42 27

41 53 55 48 32

42 44 40 36 37

a)

Construct a stem-and-leaf display.

b) Find the 5 number summary for this data set.

3. A computer password is formed by 4 characters, the characters can be numbers or letters,

(consider there are 26 letters in the alphabet). In how many ways can the password be formed?


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4. Sixty percent of the student body at UTC is from the state of Tennessee (T), 30% percent are

from other states (O), and the remainder are international students (I). Twenty percent of

students from Tennessee live in the dormitories, whereas, 50% of students from other states livein the dormitories. Finally, 80% of the international students live in the dormitories.

Given that a student lives in the dormitory, what is the probability that she/he is an international

student?

5. A production process produces 2% defective parts. A sample of five parts from the production

process is selected. What is the probability that the sample contains exactly two defectiveparts?


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6. In the season of telephone registration in a local university, calls arrive with a frequency of one

every two minutes. What is the probability to have at least3 calls in five minutes?

7. A professor at a local university noted that the grades of her students were normally distributedwith a mean of 73 and a standard deviation of 11. DO NOT ROUND YOUR NUMBERS.If 69.5 percent of the students received grades of C or better, what is the minimum score of

those who received Cs?


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8. In a city, 25% of the people prefer a specific brand of soft drink. If a sample of 200 people is

taken, what is the probability that the sample proportion of people preferring this brand is

within 0.03 of the population proportion?

9. A sample of 100 cans of coffee showed an average weight of 13 ounces with a standarddeviation of 0.8 ounces. Construct a 95% confidence interval for the mean of the population.


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10. A local health center noted that in a sample of 400 patients 80 were referred to them by the

local hospital.

a. Provide a 95% confidence interval for the proportion of all the patients who are referred tothe health center by the hospital.

b. What size sample would be required to estimate the proportion of hospital referrals with a

margin of error of 0.08 or less at 95% confidence?


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11. A soft drink filling machine, when in perfect adjustment, fills the bottles with 12 ounces of soft

drink. A random sample of 25 bottles is selected, and the contents are measured. The sample

yielded a mean content of 11.88 ounces, with a standard deviation of 0.24 ounces. Is thisevidence enough to conclude that the mean filling amount is not the target value? Solve the

problem by means of a statistical test, stating clearly the hypotheses being tested and the

conclusion you get. Use a significance level of 0.05

sample of mid term exam

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