Probability & Statistics Flashcards

Key Concepts in Probability & Statistics

• 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.

• 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

• 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.

• Qualitative Data: Not applicable for the examples given, but qualitative data would relate to descriptive attributes rather than numerical figures.

Levels of Measurement

• Nominal Level: Used for data that can be categorized by names or labels, such as colors.

• Ratio Level: Relevant for measurable quantities where an absolute zero exists, such as the ages of students.

• Ordinal Level: Involves data that can be ordered or ranked, such as movie ratings from poor to excellent.

• Interval Level: For data with meaningful intervals but no true zero, exemplified by the temperature of refrigerators.

Population vs. Sample

• Population: The complete set of all outcomes, responses, measurements, or counts of interest.

• Sample: A smaller subset extracted from the population, which is measured to draw conclusions about the population.

Parameters and Statistics

• Population Parameter: A value summarizing a characteristic of a population.

• 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

• Mean: For the data set 71, 67, 67, 72, 76, 72, 73, 68, 72, 72, the mean is calculated to be 71.

• Median: The middle value in the same dataset is the median, which is 72.

• Mode: The mode, or most frequently occurring value in the sample, is also 72.

Critical Values and Errors

• 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.

• 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

• 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.

• 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.