Samples, Standard Error of the Mean, & Confidence Intervals

Report the values you are using for this assignment

HR Mean (HR) (one decimal)	HR Std Dev (sHR) (two decimals)	RR Mean (RR) (one decimal)	RR Std Dev (sRR) (two decimals)
90	12.87	23	3.87

Task 1: Standard Error of the Mean (SEM) for Different Sample Sizes

Calculate SEM based on the population standard deviation of your 10 measures and imagine that you took samples of n=4 and n=9 from your population. Then calculate the SEM for an imaginary (impossible) sample of 100. Round the SEM value to 2 decimals for each calculation.

Formula: Standard Error of the Mean (SEM ors_M or)=

SEM	Heart Rate	Respiratory Rate
SEM if n = 4	6.44	1.94
SEM if n = 9	4.29	1.29
SEM if n= 100	1.29	0.39

What happens to the value of the SEM as the sample size increases?

The value of SEM decreases when the sample size increases.

Task 2: Lowest or Highest Boundary Points

You want to know the value the divides a certain percentage of the expected sample means from rest. Use the SEM calculated in Task 1 for a sample n=4, taken from your small population. For HR you are interested in the lowest 33%.

For RR you are interested in the highest 10%.

HR	SEM for n=4	Z for 33%	Z * SEM	Value - [Z*SEM]
6.44

RR	SEM for n=4	Z for 10%	Z * SEM	Value + [Z*SEM]
1.94

Task 3: 95% Confidence Intervals

Use the SEM calculated in Task 1 to build a 95% Confidence interval for a sample of n=9, taken from your small population. First table is for the prep calculations. Second table displays the final values somewhat visually: you could picture a normal curve and number line above the table. This may help you decide whether the sample means mentioned would be expected to fall within the 95% CI based on your population mean.

95% Confidence Interval for HR

SEM for n=9	Z for 95% CI	Z * SEM
4.29

Lower Limit - [Z*SEM]	Mean	Upper Limit + [Z*SEM]

Would a sample mean of 81.7 fall within the 95% CI for HR?

95% Confidence Interval for RR

SEM for n=9	Z for 95% CI	Z * SEM
1.29

Lower Limit - [Z*SEM]	Mean	Upper Limit + [Z*SEM]

Would a sample mean of 14.2 fall within the 95% CI for RR?