Questions and Answers
The average age of the students in a statistics class is 17 years. Does this statement describe?
From past figures, it is predicted that 14% of the registered voters in California will vote in the June primary. Does this describe?
Classify the number of seats in a movie theater as qualitative data or quantitative data.
Classify the number on the shirts of a girl's soccer team as qualitative data or quantitative data.
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Identify the level of measurement for data that can be classified according to color.
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Identify the level of measurement for data that are the ages of students in a statistics class.
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Identify the level of measurement for data that are the ratings of a movie ranging from poor to excellent.
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Identify the level of measurement for data that are the temperature of 53 refrigerators.
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Explain the difference between a sample and a population.
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A recent survey by the alumni of a major university indicated that the average salary of 7000 of its 225,000 graduates was 110,000. Does this value describe a population parameter or a sample statistic?
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Find the mean of the following data: 71, 67, 67, 72, 76, 72, 73, 68, 72, 72.
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Find the median of the following data: 71, 67, 67, 72, 76, 72, 73, 68, 72, 72.
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Find the mode of the following data: 71, 67, 67, 72, 76, 72, 73, 68, 72, 72.
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Find the critical value, tc for c=0.99 and n=10.
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Find the critical value, tc for c=0.95 and n=16.
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Find the value of E, the maximum error of estimate for c=0.90, n=16 and s=2.5.
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The standard IQ test has a mean of 101 and a standard deviation of 16. We want to be 98% certain that we are within 4 IQ points of the true mean. Determine the required sample size.
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A random sample of 40 students has a mean annual earnings of $3120 and a standard deviation of $677. Find the margin of error if c=0.95.
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A random sample of 120 students has a test score average with a standard deviation of 9.2. Find the margin of error if c=0.98.
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Find the critical value zc that corresponds to a 95% confidence level.
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Study Notes
Key Concepts in Probability & Statistics
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Inferential Statistics: Utilized when describing that the average age of students in a statistics class is 17 years. This involves making predictions or generalizations about a population based on sample data.
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Descriptive Statistics: Application of statistics to summarize past figures, such as predicting a 14% voter turnout for registered voters in California during the June primary.
Data Classification
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Quantitative Data: Examples include the number of seats in a movie theater and the shirt numbers of a soccer team. This type of data is numerical and can be measured.
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Qualitative Data: Not applicable for the examples given, but qualitative data would relate to descriptive attributes rather than numerical figures.
Levels of Measurement
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Nominal Level: Used for data that can be categorized by names or labels, such as colors.
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Ratio Level: Relevant for measurable quantities where an absolute zero exists, such as the ages of students.
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Ordinal Level: Involves data that can be ordered or ranked, such as movie ratings from poor to excellent.
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Interval Level: For data with meaningful intervals but no true zero, exemplified by the temperature of refrigerators.
Population vs. Sample
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Population: The complete set of all outcomes, responses, measurements, or counts of interest.
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Sample: A smaller subset extracted from the population, which is measured to draw conclusions about the population.
Parameters and Statistics
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Population Parameter: A value summarizing a characteristic of a population.
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Sample Statistic: Refers to values calculated from sample data. The average salary of 7000 graduates taken from a total of 225,000 reflects a sample statistic.
Statistical Measures
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Mean: For the data set 71, 67, 67, 72, 76, 72, 73, 68, 72, 72, the mean is calculated to be 71.
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Median: The middle value in the same dataset is the median, which is 72.
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Mode: The mode, or most frequently occurring value in the sample, is also 72.
Critical Values and Errors
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Critical Value (tc): For a confidence level of 99% with a sample size of 10, tc is 3.250. For a 95% confidence level with 16 degrees of freedom, tc is 2.131.
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Maximum Error of Estimate (E): For confidence level 90%, sample size 16, and standard deviation 2.5, E equals 1.1.
Sample Size and Margin of Error
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Sample Size Determination: To be 98% certain of being within 4 IQ points of the mean with a standard IQ test mean of 101 and standard deviation of 16, a sample size of 87 is required.
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Margin of Error: For a random sample of 40 students with mean annual earnings of $3120 and standard deviation of $677, the margin of error at a 95% confidence level is $217.3. For a sample of 120 students with a standard deviation of 9.2 at a confidence level of 98%, the margin of error is 1.985.
Confidence Levels
- Critical Value for Confidence Level: For a 95% confidence level, the critical z-values are +1.96 and -1.96.
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Description
Test your knowledge of key concepts in Probability and Statistics with these flashcards. Each card presents a statement or scenario that you'll classify as either inferential or descriptive statistics. Perfect for final exam preparation!
