Podcast
Questions and Answers
What is the sample mean resting pulse rate for non-exercisers?
What is the sample mean resting pulse rate for non-exercisers?
- 28 bpm
- 66 bpm
- 75 bpm (correct)
- 9.0 bpm
What is the sample standard deviation for exercisers?
What is the sample standard deviation for exercisers?
- 29
- 8.6 (correct)
- 9.0
- 66
What is the degree of freedom used for the confidence interval calculation in this study?
What is the degree of freedom used for the confidence interval calculation in this study?
- 50 (correct)
- 28
- 58
- 29
What multiplier t* is used for large samples (n1 + n2 = 60)?
What multiplier t* is used for large samples (n1 + n2 = 60)?
What does the confidence interval of 4.435 bpm to 13.565 bpm represent?
What does the confidence interval of 4.435 bpm to 13.565 bpm represent?
What conclusion can be drawn since 0 is not in the confidence interval?
What conclusion can be drawn since 0 is not in the confidence interval?
Which statistical procedure can be used because of the large sample sizes involved?
Which statistical procedure can be used because of the large sample sizes involved?
What is the total number of subjects in both samples combined?
What is the total number of subjects in both samples combined?
Which group had a lower mean resting pulse rate?
Which group had a lower mean resting pulse rate?
If using the conservative degrees of freedom method, what is the conservative df calculated?
If using the conservative degrees of freedom method, what is the conservative df calculated?
What is required for two samples to be considered independent?
What is required for two samples to be considered independent?
Which of the following statements about the populations from which the samples are drawn is true?
Which of the following statements about the populations from which the samples are drawn is true?
How are paired samples different from independent samples?
How are paired samples different from independent samples?
What must hold true about the shapes of data distributions in independent samples?
What must hold true about the shapes of data distributions in independent samples?
In which scenario would matching individuals in two samples violate independence?
In which scenario would matching individuals in two samples violate independence?
Which of the following is a key characteristic of two-independent samples?
Which of the following is a key characteristic of two-independent samples?
What is an essential requirement for the populations from which independent samples are drawn?
What is an essential requirement for the populations from which independent samples are drawn?
Which of the following factors does NOT affect the independence of two samples?
Which of the following factors does NOT affect the independence of two samples?
When conducting inference on means from two samples, what must be true about the variables measured?
When conducting inference on means from two samples, what must be true about the variables measured?
What is the main assumption for the validity of t-procedures for two independent samples?
What is the main assumption for the validity of t-procedures for two independent samples?
When is it appropriate to use t-procedures for small sample sizes?
When is it appropriate to use t-procedures for small sample sizes?
What is the conservative approach for calculating degrees of freedom (df) in independent samples?
What is the conservative approach for calculating degrees of freedom (df) in independent samples?
In what scenario can t-procedures be used for large samples?
In what scenario can t-procedures be used for large samples?
What characteristic of the data sets affects the decision to use t-procedures for medium sample sizes?
What characteristic of the data sets affects the decision to use t-procedures for medium sample sizes?
To ensure an accurate estimate using a full degrees of freedom approximation, what should be verified?
To ensure an accurate estimate using a full degrees of freedom approximation, what should be verified?
Which sample sizes allow using t-procedures with clearly skewed distributions?
Which sample sizes allow using t-procedures with clearly skewed distributions?
Which condition is least important for independent samples when using t-procedures?
Which condition is least important for independent samples when using t-procedures?
What can invalidate the use of t-procedures regardless of sample size?
What can invalidate the use of t-procedures regardless of sample size?
What is a necessary condition for small sample sizes when data is skewed?
What is a necessary condition for small sample sizes when data is skewed?
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Study Notes
Two-Independent-Sample Problems
- Comparing the mean resting pulse rate of adult subjects who regularly exercise to those who do not.
- We have two independent random samples from two distinct populations.
- The two samples are assumed to be independent and can be of different sizes.
- We assume both population distributions are Normal.
- We can use t-procedures for two independent samples.
Conditions for Independent Samples
- The assumption that each sample is an independent random sample from the population of interest is more important than the assumption that the two population distributions are Normal.
- For small sample sizes (n1 + n2 < 15), each data set must be close to Normal.
- For medium sample sizes (n1 + n2 ≥ 15), t procedures are okay except in the presence of outliers or strong skewness.
- For large samples (n1 + n2 ≥ 40), t procedures can be used even for skewed distributions.
Confidence Interval for Independent Samples
- The full df approximation gives more accurate results than the conservative approach.
- When calculating by hand, use the conservative approach: df = the smaller of (n1 – 1) or (n2 – 1).
- Leave the full df calculation for software to do.
Exercise and Pulse Rates Example
- A study compared the mean resting pulse rates of adult subjects who regularly exercise to those who don't.
- We can use the t-procedure since the sample sizes are large (n1 + n2 = 60).
- The conservative df is 28.
- The multiplier t* is 2.048.
- The 95% confidence interval for the difference in population means is between 4.435 bpm and 13.565 bpm.
- Since 0 is not in the confidence interval, we can claim there is a difference in the mean resting pulse rates between non-exercisers and exercisers.
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