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Introductory Statistics > Confidence And Significance And Sampling And Error > Flashcards

Confidence And Significance And Sampling And Error Flashcards

1
Q

What is a variable in statistics?

A

A characteristic that varies from one individual to another in a population.

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2
Q

Why do we use samples in statistics?

A

To draw conclusions about a larger population without measuring every individual.

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3
Q

What is sampling error?

A

The variation in summary statistics derived from different samples due to randomness.

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4
Q

What is the population mean (μ) in the given example?

A

2.66 hours.

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5
Q

What is the sample mean (𝑥̅) in the given example?

A

2.72 hours.

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6
Q

What are the two primary types of errors that can affect statistical estimates?

A
  • Random Error (Noise) * Systematic Error (Bias)
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7
Q

Characteristics of random error include:

A
  • Unpredictable * Fluctuates in both directions * Caused by unknown factors.
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8
Q

Characteristics of systematic error include:

A
  • Consistent * Predictable * Caused by flaws in study design.
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9
Q

What does the term ‘population parameter’ refer to?

A

The true value we want to estimate, such as the population mean.

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10
Q

What does the term ‘sample statistic’ refer to?

A

The estimate of the parameter derived from the sample data.

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11
Q

What is the standard deviation (σ) of the population in the example?

A

0.564.

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12
Q

What is the sample size used in the example?

A

14.

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13
Q

What is the Central Limit Theorem (CLT)?

A

States that the sampling distribution of the sample means will approach a normal distribution as the sample size increases.

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14
Q

True or False: The sampling distribution has a mean equal to the population mean (μ).

A

True.

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15
Q

What is the definition of standard error (SE)?

A

A measure of how far the sample mean is likely to be from the true population mean.

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16
Q

Fill in the blank: The sampling distribution of the mean approaches a _______ distribution as the sample size becomes large.

A

[normal]

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17
Q

What is a confidence interval (CI)?

A

A range of values that estimates the true value of a population parameter.

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18
Q

What is the significance of a p-value of 0.03 in hypothesis testing?

A

Indicates a 3% probability that the observed difference occurred by chance, suggesting a significant effect.

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19
Q

What does the term ‘sampling distribution’ refer to?

A

The distribution of sample statistics across many samples.

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20
Q

What is the variance of the population in the example?

A

0.318.

21
Q

What does a normal distribution indicate about the data?

A

The mean, median, and mode are equal, and data clusters around the mean.

22
Q

In a normal distribution, what percentage of data falls within 1 standard deviation of the mean?

A

68%.

23
Q

What is the formula for calculating standard error?

A

SE = σ / √n.

24
Q

What is the mean of the sample mean distribution compared to the population mean?

A

They are approximately equal.

25
Q

True or False: Systematic error always occurs in one direction.

A

True.

26
Q

What is the standard deviation of the sample in the example?

A

0.623.

27
Q

What happens to the standard error as the sample size increases?

A

It becomes smaller.

28
Q

What is the importance of proper sampling techniques?

A

To ensure that the sample is representative of the population.

29
Q

What is an example of a systematic error in sampling?

A

Selecting participants only outside a gym.

30
Q

What is the proportion of the population exercising more than 3 hours per week?

A

0.29.

31
Q

What is the sample proportion of people exercising more than 3 hours per week?

A

0.36.

32
Q

What does the sampling distribution of the mean illustrate?

A

The means of different samples drawn from the same population.

33
Q

What is a confidence interval?

A

A range of values that estimates the true value of a population parameter

34
Q

What does a 95% confidence interval indicate?

A

The researcher is 95% confident that the true average lies within the interval

35
Q

What is the Central Limit Theorem?

A

The sampling distribution of the sample mean approaches a normal distribution as the sample size increases

36
Q

What does the mean of the sampling distribution equal?

A

The population mean

37
Q

What is the standard deviation of the sampling distribution called?

A

Standard Error (SE)

38
Q

What is needed to calculate a confidence interval?

A

Sample mean (x̄), standard deviation (s), sample size (n)

39
Q

What does a wider confidence interval indicate?

A

More uncertainty about the estimate

40
Q

What does a narrower confidence interval suggest?

A

Greater precision

41
Q

True or False: A 95% confidence level means that approximately 95 out of 100 intervals will contain the true population mean.

A

True

42
Q

What happens when the confidence level is increased (e.g., to 99%)?

A

The interval widens, reflecting increased certainty at the expense of precision

43
Q

Fill in the blank: The confidence interval provides a range likely to contain the true _______.

A

population mean

44
Q

What analogy is used to explain confidence intervals?

A

The candy bowl analogy, where wider spoons (wider CIs) are more likely to scoop up the true population parameter but less precise

45
Q

What is the first step to calculate confidence intervals in SPSS?

A

Open SPSS and input your data

46
Q

What menu path is followed in SPSS to calculate confidence intervals?

A

Analyze → Descriptive Statistics → Explore

47
Q

What should be checked in SPSS to ensure confidence intervals for the mean are calculated?

A

Ensure ‘Confidence Interval for the Mean’ is checked

48
Q

What is the relationship between confidence and precision in confidence intervals?

A

Wider intervals provide more confidence but less precision, while narrower intervals provide more precision but less confidence

49
Q

What is the purpose of confidence intervals in statistical analysis?

A

To provide insights into the reliability of sample estimates

Introductory Statistics (7 decks)

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