Section 1.1 Notes complete(1) (1)
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Math 1442 (Statistics for Life)
Ch 1
Sec 1.1
Section 1.1 Statistical and Critical Thinking
DEFINITIONS
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Math 1442 (Statistics for Life)
Ch 1
Sec 1.1
Example 2: Identify the population and the sample in the following study.
A study of the dietary habits of 20,000 men was conducted to find a link between high intakes of dairy products and prostate cancer. Example 3: Would you collect data using a population (a census) or a sample (a sampling) to determine the following? Why?
a)
The most popular sports team among people in New York. b)
The average salary of the 30 employees of a company. c)
Whether wedding guests are allergic to the planned main course. d)
Amount of time high school students spend on their cell phones each week. Example 4: Determine if each of the following is a population parameter or a sample statistic.
a)
A survey of 1000 U.S. adults found that 40% think that the Internet is the best way to get news and information. b)
At a college, 90% of the members of the Board of Trustees approved the contract of the new president. c)
A survey of 733 small business owners found that 17% have a current job opening. 2
Math 1442 (Statistics for Life)
Ch 1
Sec 1.1
d)
The 2182 students who accepted admission offers to Northwestern University in 2009 have an average SAT score of 1442. (Source: Northwestern University)
Example 5:
In a recent survey, 1500 adults in the United States were asked if they thought there was solid evidence for global warming. Eight hundred fifty-five of the adults said yes. (Adapted from: Pew Research Center). Identify the population and the sample. Describe the data set
The Process of Statistical Study: Prepare → Analyze → Conclude (P.A.C.)
Voluntary Response Sample (or Self-Selected Sample):
one in which the respondents themselves decide whether to be included.
Example: Internet polls, in which people online can decide whether to respond : Mail-in polls, in which people can decide whether to reply : Telephone call-in polls, in which newspaper, radio, or television announcements ask that you voluntarily call a special number to register your opinion
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Math 1442 (Statistics for Life)
Ch 1
Sec 1.1
Potential Pitfalls(problems) when analyzing data
• Misleading conclusions
: When forming a conclusion based on a statistical analysis, we should make statements that are clear even to those who have no understanding of statistics and its terminology. We should carefully avoid making statements not justified by the statistical analysis.
• Correlation does not imply causation
: Two things may be related but it does not mean one causes the other to happen.
• Sample data reported instead of measures
: When collecting data from people, it is better to take measurements yourself instead of asking subjects to
report
results.
• Small samples
: When a school suspension rate is based on 10 samples
• Loaded questions
: If survey questions are not worded carefully, the results of a study can be misleading. Survey questions can be “loaded,” or intentionally worded to elicit a desired response.
• Order of questions
: Sometimes survey questions are unintentionally loaded by such factors as the order of the items being considered.
• Nonresponse
: A
nonresponse
occurs when someone either refuses to respond to a survey question or is unavailable.
• Percentages
: Some studies cite misleading or unclear percentages. Note that 100% of some quantity is
all
of it, but if there are references made to percentages that exceed 100%, such references are often not justified.
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Math 1442 (Statistics for Life)
Ch 1
Sec 1.1
* How to calculate percentage: % means “divide by 100”
i.e. 6% of 1200 = _______________________ i.e. 4 students out of 20 = ____________________
i.e. 7 students out of 22 = _____________________
Statistical Significance
: achieved in a study if the likelihood of an event occurring by chance is 5% or less.
Practical Significance
: It is possible that some treatment or finding is effective, but common sense might suggest that the treatment or finding does not make enough of a difference to justify its use or to be practical.
Example 6:
In the followings, determine whether the results appear to have statistical significance, and also determine whether the results appear to have a practical significance. (a)
In a study of the Gender Aide method of gender selection used to increase the likelihood of a baby being
born a girl, 2000 users of the method gave birth to 980 to 1020 girls. There is about a 3% chance that many girls if the method had no effect. 5
Math 1442 (Statistics for Life)
Ch 1
Sec 1.1
(b) When making random guesses for difficult multiple-choice test questions with possible answers of a, b, c, d, and e, we expect to get about 20% of the answer correct. The Ashton Prep Program claims to have developed a better method of guessing. In a test of that program, guesses were made for 100 answers, and 23 were found to be correct. There is a 23% chance of getting such results if the program has no effect.
(c)
IQ Scores
Most people have IQ scores between 70 and 130. For $39.99, you can purchase a PC or Mac program from HighIQPro that is claimed to increase your IQ score by 10 to 20 points. The program claims to be “the only proven IQ increasing software in the brain training market,” but the author of your text could find no data supporting that claim, so let's suppose that these results were obtained: In a study of 12 subjects using the program, the average increase in IQ score is 3 IQ points. There is a 25% chance of getting such results if the program has no effect.
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