# A number of question & solutions about data and data rates

This is more along the lines of computer driven word questions, but figured my best bet for asisstance would be the Math section. That is why it is being posted here.

Answer ONLY 5 of the questions attached for 6 custom credits.

Pick any 5

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#### Solution Preview

(1)

Sociologists can get three possible answers to a typical survey question such as "Do you believe in the tooth fairy?" -namely, yes, no, and no opinion. With this in mind, the Sociomagnetic Computer Company has decided to build a computer to process survey data. This computer has a trinanry of memory-that is, each byte (tryte?) consists of 8 trits, with a trit holding a 0, 1, or 2. How many trits are needed to hold a 6-bit number? Give an expression for the number or trits needed to hold n bits.

A 6 bit number has 26 = 64 possible combinations

As a trit consists of 3 states 0,1 or 2 so we need to use modular 3 arithmetic to determine how many trits (N) are required to store any 6 bit number

We therefore need to solve the equation

3^N >= 64 (1)

Taking Logs to base 10 each side of (1) we get

Log{3}^N >= Log{64}

N*Log{3} >= Log{64}

N >= Log{64}/Log{3}

N >= 1.806/0.477

N >= 3.785

As we can only consider whole integers for N, the number of trits needed to store a 6 bit number must be at least N = 4

In order to store n bits we can develop a similar expression to one noting that the number n of binary bits can store 2n decimal numbers

Thus we say that 3^N >= 2^n (2)

Again taking Logs to base 10 of both sides of (2) we get

N*Log{3} >= n*Log{2}

Thus the number of trits (N) necessary to fully express an n bit number is given by (3)

N >= n*Log{2}/Log{3} (3) {where N is the rounded up to the next whole integer}

(2)

Compute the data rate of the human ear from the following information. People can hear ...

#### Solution Summary

A number of questions are presented about data, data rates and data storage and compression and work examples to those question are presented. 5 such questions are presented and solutions provided

Stats questions

1) If an experiment results in data that are continuous in nature, must the data also be quantitative, or can they be qualitative?

2) A sample of Americans is selected and the average (mean) amount of time watching television is 4. 6 hours per day. Is the value statistic or parameter?

3) In New York City, there are 3250 walk buttons that pedestrians can press at traffic intersections, and 2500 of them do not work. Is the value discrete or continuous?

4) In a survey of 1059 adults, it is found that 39% of them have guns in their homes. Is the value discrete or continuous?

5) Consumer Reports magazine ratings of best buy, recommended, not recommended. Is the level of measurement nominal, ordinal, interval or ratio?

6) Salaries of women who are chief executive officers of corporations. Is the level of measurement nominal, ordinal, interval or ratio?

7) The current temperatures in the 50 state capitol cities. Is the level of measurement nominal, ordinal, interval or ratio?

8) During the superbowl game, a survey of 5108 randomly selected households finds that 44% of them have television sets tuned to the superbowl. What are the sample and the population? Is the sample likely to be representative of the population?

9) A graduate student at the University of Newport conducts a research project about communication. She mails a survey to all of the 500 adults that she knows. She asks them to mail back a response to this question: Do you prefer to use email or snail mail? She gets back 65 responses, with 42 of them indicating a preference for snail mail. What are the sample and the population? Is the sample likely to be representative of the population?

10) A group of students develops a scale for rating the quality of the cafeteria food, with 0 representing "neutral: not good and not bad. Bad meals are given negative numbers and good meals are given positive numbers, with the magnitude of the number corresponding to the severity of badness or goodness. The first three meals are rated as 2, 4, and -5. What is the level of measurement for such ratings?

11) The phone rings and an automated voice asks whether you are willing to vote for a candidate with a long history of raising taxes and wasting taxpayer money. Assuming that the calls are made to randomly selected voters, are the results likely to reflect the preference that voters have for this candidate?

12) Based on a study showing that college graduates tend to live longer than those who do not graduate from college, a researcher concludes that studying cause people to live longer. Develop an alternative conclusion.

13) The author received a survey from the investment firm of Merrill Lynch. It was designed to gauge his satisfaction as a client, and it had specific questions for rating the author's personal Financial Consultant. The cover letter included this statement: Your responses are extremely valuable to you Financial Consultant, Russell R. Smith, and to Merrill Lynch...We will share your name and response with your Financial Consultant. What is wrong with this survey? Develop an alternative conclusion.

14) Conversions

a. What is 15% of 620?

b. Convert 5% to an equivalent decimal

c. Convert 0.01 to an equivalent percentage

d. Convert the fraction 987/1068 to an equivalent percentage. Express to the nearest tenth of a percent.

15) In a study of the cholesterol drug Lipitor, 270 patients were given a placebo, and 19 of those 270 patients reported headaches. What percentage of this placebo group reported headaches?

16) Among the 270 patients in the placebo group, 3.0% reported back pains. What is the actual number of patients who reported back pains?

17) When conducting an experiment to test the effectiveness of a new vaccine, a researcher chooses to use blocking, with men in one block and women in another block. How does this use of blocking help the experiment?

18) Cruise ship passengers are given magnetic bracelets, which they agree to wear in an attempt to eliminate or diminish the effects of motion sickness. Is this a an observational study or an experiment?

19) An economist collects income data by selecting and interviewing subjects now, then going back in time to see if they had the wisdom to take a statistics course between the years of 1980 and 2005. Is this a cross-sectional, retrospective or prospective?

20) On days of presidential elections, the news media organize and exit poll in which specific polling stations are randomly selected and all voters are surveyed as they leave the premises. Is this random, systematic, convenience, stratified or cluster?

21) An engineering student measures the strength of fingers used to push buttons by testing family members. Is this random, systematic, convenience, stratified or cluster?

22) Fund raisers for the College of Newport test a new telemarketing campaign by obtaining a list of alumni and selecting every 100th name on that list. Is this random, systematic, convenience, stratified or cluster?

23) A statistics professor obtains a sample of students by selecting the first 10 students entering her classroom. Does this sampling plan result in a random sample or simple random sample?

24) A researcher for the Orange County Department of Motor Vehicles plans to test a new online driver registration system by using a sample consisting of 20 randomly selected men and 20 randomly selected women. Does this sampling plan result in a random sample or simple random sample?

25) An inspector for the US FDA obtains vitamin pills produced in an hour at the Health Supply Company. She thoroughly mixes them, then scoops a sample of 10 pills that are to be tested for the exact amount of vitamin content. Does this sampling plan result in a random sample or simple random sample?