Confidence And Significance And Sampling And Error

Question 1

What is a variable in statistics?

Answer 1

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

Question 2

Why do we use samples in statistics?

Answer 2

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

Question 3

What is sampling error?

Answer 3

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

Question 4

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

Answer 4

2.66 hours.

Question 5

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

Answer 5

2.72 hours.

Question 6

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

Answer 6

• Random Error (Noise) * Systematic Error (Bias)

Question 7

Characteristics of random error include:

Answer 7

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

Question 8

Characteristics of systematic error include:

Answer 8

• Consistent * Predictable * Caused by flaws in study design.

Question 9

What does the term ‘population parameter’ refer to?

Answer 9

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

Question 10

What does the term ‘sample statistic’ refer to?

Answer 10

The estimate of the parameter derived from the sample data.

Question 11

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

Answer 11

0.564.

Question 12

What is the sample size used in the example?

Answer 12

14.

Question 13

What is the Central Limit Theorem (CLT)?

Answer 13

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

Question 14

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

Answer 14

True.

Question 15

What is the definition of standard error (SE)?

Answer 15

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

Question 16

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

Answer 16

[normal]

Question 17

What is a confidence interval (CI)?

Answer 17

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

Question 18

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

Answer 18

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

Question 19

What does the term ‘sampling distribution’ refer to?

Answer 19

The distribution of sample statistics across many samples.

Question 20

What is the variance of the population in the example?

Answer 20

0.318.

Question 21

What does a normal distribution indicate about the data?

Answer 21

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

Question 22

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

Answer 22

68%.

Question 23

What is the formula for calculating standard error?

Answer 23

SE = σ / √n.

Question 24

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

Answer 24

They are approximately equal.

Question 25

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

Answer 25

True.

Question 26

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

Answer 26

0.623.

Question 27

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

Answer 27

It becomes smaller.

Question 28

What is the importance of proper sampling techniques?

Answer 28

To ensure that the sample is representative of the population.

Question 29

What is an example of a systematic error in sampling?

Answer 29

Selecting participants only outside a gym.

Question 30

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

Answer 30

0.29.

Question 31

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

Answer 31

0.36.

Question 32

What does the sampling distribution of the mean illustrate?

Answer 32

The means of different samples drawn from the same population.

Question 33

What is a confidence interval?

Answer 33

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

Question 34

What does a 95% confidence interval indicate?

Answer 34

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

Question 35

What is the Central Limit Theorem?

Answer 35

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

Question 36

What does the mean of the sampling distribution equal?

Answer 36

The population mean

Question 37

What is the standard deviation of the sampling distribution called?

Answer 37

Standard Error (SE)

Question 38

What is needed to calculate a confidence interval?

Answer 38

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

Question 39

What does a wider confidence interval indicate?

Answer 39

More uncertainty about the estimate

Question 40

What does a narrower confidence interval suggest?

Answer 40

Greater precision

Question 41

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

Answer 41

True

Question 42

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

Answer 42

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

Question 43

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

Answer 43

population mean

Question 44

What analogy is used to explain confidence intervals?

Answer 44

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

Question 45

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

Answer 45

Open SPSS and input your data

Question 46

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

Answer 46

Analyze → Descriptive Statistics → Explore

Question 47

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

Answer 47

Ensure 'Confidence Interval for the Mean' is checked

Question 48

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

Answer 48

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

Question 49

What is the purpose of confidence intervals in statistical analysis?

Answer 49

To provide insights into the reliability of sample estimates