Statistical Concepts Review for Exam 1

Introduction to Statistics Review for Exam 1

Survey Analysis of Television Viewing Habits

  1. Online Survey about Television Viewing

    • Conducted by a leading cable industry provider in June.

    • Sample Size: 2,029 American adults aged 18 and older.

    • Population of Interest: 1,958 adults actively watching television.

    • Key Findings:

      • 72% watch cable TV.

      • 33% watch on devices (tablet, smartphone, or computer).

  2. Parameters of Interest

    • Parameter of Interest: The population attribute or characteristic that is being measured.

    • Population of Interest: All American adults aged 18 or older who watch television.

    • Sample: The 2,029 American adults surveyed.

  3. Analysis of Statistics

    • Statement 72% watch cable TV:

      • Parameter or Statistic: This is a statistic because it is derived from a sample rather than the entire population.

      • Descriptive or Inferential: It is descriptive as it describes the sample data.

    • Estimate of regional internet provider:

      • Viewership: 726,000 of 2.2 million viewers apparently watch TV on devices.

      • Estimated Percentage:
        rac{726,000}{2,200,000} imes 100 ext{ (as a percentage) } = 33 ext{%}

      • Descriptive or Inferential: This is inferential since it extends the finding to a population.

Study Practices of CSCC Students

  1. Research Inquiry

    • Objective: Determine study practices of CSCC students through sampling.

    • Sample Size: 100 students.

  2. Population and Sample

    • Population: All CSCC students.

    • Sample: The 100 students surveyed for study habits.

  3. Proportional Data

    • Mathematics Subject Response: 58 out of 100 students indicated mathematics as the subject taking the longest time to study.

      • Parameter or Statistic: This is a statistic as it is a measure derived from sample data.

  4. Statement Analysis

    • Assessment:

      • True or False statement regarding data (c):

      • Original: "Data from part (c) is both quantitative and discrete."

      • Correction: This is False because the response regarding subjects is categorical, not quantitative.

  5. Variable Examples
    (Examples of each variable type potentially collected)

    • Ordinal Variable: Satisfaction Level (Low, Medium, High)

    • Interval Variable: Hours spent studying by students.

    • Nominal Variable: Course names or types (e.g., Mathematics, History).

  6. Sampling Methods

    • Simple Random Sample: Randomly selecting 100 students from the entire population.

    • Systematic Sampling: Perhaps selecting every 10th student from the population once ordered.

    • Stratified Sampling: Dividing students into strata based on majors and randomly sampling from each.

    • Cluster Sampling: Dividing the school into groups (e.g., classes) and randomly selecting entire classes.

    • Convenience Sampling: Surveying students who are easily accessible (e.g., those in a common area).

  7. Skewness in Study Data

    • Right Skewed Distribution: More students spend short periods on studies while fewer study for long durations; would expect such a result due to varied study habits.

  8. Graph Types for Data Representation

    • Locations where students study: Use a bar chart (categorical).

    • Hours spent studying: Histogram (continuous data).

    • Course taking the most study time: Pie chart (proportional data).

    • Number of credit hours taken this quarter: Histogram (continuous data).

Sampling Methods Identification

  1. Identify the Sampling method (Questions 3-8)

    1. Cluster Sample: Survey from groups of new car buyers by brand.

    2. Convenience Sampling: Surveying first 100 airport passengers.

    3. Simple Random Sample: Drawing 1,000 calls randomly from total calls made.

    4. Systematic Sampling: Testing every 1000th cell phone produced.

    5. Voluntary Response Sampling: Surveys on receipts from customers.

    6. Cluster Sampling: Randomly selecting neighborhoods and surveying all homes.

Variables and Data Qualities

  1. Examples Classification (Examples 9-12)

    1. OSU Basketball Ranking: Ordinal, Qualitative

    2. Telephone Number: Nominal, Qualitative

    3. Oven Temperature: Continuous, Quantitative

    4. Heights of Women: Continuous, Quantitative

    5. Number of TVs: Discrete, Quantitative.

Distribution Analysis

  1. Determine shapes and sampling for distributions (Question 10a-b)

    1. Distribution Shape for SUV gas mileage: Skewed Left; Mean < Median.

    2. Distribution Shape for hybrid cars: Skewed Right; Mean > Median.

  2. Study Classification (Experiment vs. Observational)

    1. Observational study: Nancy watching toddlers.

    2. Experimental setting: Beth's blood pressure comparison.

  3. Parameter/Statistic Definitions (Question 11)

    1. All Ohio registered voters: Population

    2. Subgroup from CSCC: Sample

    3. Mean height of U.S. men: Parameter

    4. Mean height of sampled men: Statistic

Employee Survey Variables Identification

  1. Variables in Employment Survey Data (Question 11)

    • Employment Category: Categorical

    • MBA Required: Categorical (Nominal)

    • Years of Work Experience: Ordinal

    • Median Salary: Quantitative (Continuous)

Statistical Calculations and Summarizations

  1. Delta vs. US Air Ticket Prices

    • Calculate central tendencies: Mean, Median for data sets.

    • Identify skews: Right-skewed when Mean > Median; and vice versa for left.

    • Compare sensitivity through standard deviation calculations.

    • Create a frequency table for clear representation.

  2. Gyro Sales Analysis

    • Find Mean/Standard Deviation for grouped data; sample size: N=150N = 150.

    • Represent data visually and through histograms and charts.

Conclusion and Implications

  1. Summarize findings from statistical sampling, data analysis, and representation of survey results through appropriate graphs and statistical methods in real-world applications such as job market analysis, health data, and survey responsiveness.