Confidence And Significance And Sampling And Error Flashcards
What is a variable in statistics?
A characteristic that varies from one individual to another in a population.
Why do we use samples in statistics?
To draw conclusions about a larger population without measuring every individual.
What is sampling error?
The variation in summary statistics derived from different samples due to randomness.
What is the population mean (μ) in the given example?
2.66 hours.
What is the sample mean (𝑥̅) in the given example?
2.72 hours.
What are the two primary types of errors that can affect statistical estimates?
- Random Error (Noise) * Systematic Error (Bias)
Characteristics of random error include:
- Unpredictable * Fluctuates in both directions * Caused by unknown factors.
Characteristics of systematic error include:
- Consistent * Predictable * Caused by flaws in study design.
What does the term ‘population parameter’ refer to?
The true value we want to estimate, such as the population mean.
What does the term ‘sample statistic’ refer to?
The estimate of the parameter derived from the sample data.
What is the standard deviation (σ) of the population in the example?
0.564.
What is the sample size used in the example?
14.
What is the Central Limit Theorem (CLT)?
States that the sampling distribution of the sample means will approach a normal distribution as the sample size increases.
True or False: The sampling distribution has a mean equal to the population mean (μ).
True.
What is the definition of standard error (SE)?
A measure of how far the sample mean is likely to be from the true population mean.
Fill in the blank: The sampling distribution of the mean approaches a _______ distribution as the sample size becomes large.
[normal]
What is a confidence interval (CI)?
A range of values that estimates the true value of a population parameter.
What is the significance of a p-value of 0.03 in hypothesis testing?
Indicates a 3% probability that the observed difference occurred by chance, suggesting a significant effect.
What does the term ‘sampling distribution’ refer to?
The distribution of sample statistics across many samples.
What is the variance of the population in the example?
0.318.
What does a normal distribution indicate about the data?
The mean, median, and mode are equal, and data clusters around the mean.
In a normal distribution, what percentage of data falls within 1 standard deviation of the mean?
68%.
What is the formula for calculating standard error?
SE = σ / √n.
What is the mean of the sample mean distribution compared to the population mean?
They are approximately equal.
True or False: Systematic error always occurs in one direction.
True.
What is the standard deviation of the sample in the example?
0.623.
What happens to the standard error as the sample size increases?
It becomes smaller.
What is the importance of proper sampling techniques?
To ensure that the sample is representative of the population.
What is an example of a systematic error in sampling?
Selecting participants only outside a gym.
What is the proportion of the population exercising more than 3 hours per week?
0.29.
What is the sample proportion of people exercising more than 3 hours per week?
0.36.
What does the sampling distribution of the mean illustrate?
The means of different samples drawn from the same population.
What is a confidence interval?
A range of values that estimates the true value of a population parameter
What does a 95% confidence interval indicate?
The researcher is 95% confident that the true average lies within the interval
What is the Central Limit Theorem?
The sampling distribution of the sample mean approaches a normal distribution as the sample size increases
What does the mean of the sampling distribution equal?
The population mean
What is the standard deviation of the sampling distribution called?
Standard Error (SE)
What is needed to calculate a confidence interval?
Sample mean (x̄), standard deviation (s), sample size (n)
What does a wider confidence interval indicate?
More uncertainty about the estimate
What does a narrower confidence interval suggest?
Greater precision
True or False: A 95% confidence level means that approximately 95 out of 100 intervals will contain the true population mean.
True
What happens when the confidence level is increased (e.g., to 99%)?
The interval widens, reflecting increased certainty at the expense of precision
Fill in the blank: The confidence interval provides a range likely to contain the true _______.
population mean
What analogy is used to explain confidence intervals?
The candy bowl analogy, where wider spoons (wider CIs) are more likely to scoop up the true population parameter but less precise
What is the first step to calculate confidence intervals in SPSS?
Open SPSS and input your data
What menu path is followed in SPSS to calculate confidence intervals?
Analyze → Descriptive Statistics → Explore
What should be checked in SPSS to ensure confidence intervals for the mean are calculated?
Ensure ‘Confidence Interval for the Mean’ is checked
What is the relationship between confidence and precision in confidence intervals?
Wider intervals provide more confidence but less precision, while narrower intervals provide more precision but less confidence
What is the purpose of confidence intervals in statistical analysis?
To provide insights into the reliability of sample estimates
