Statistics Assignment: Calculating Sample Means and Standard Error

This assignment focuses on calculating sample means and standard error of M using provided data sets and population standard deviations. The assignment presents three different scenarios involving program satisfaction scores, visitations to foster children, and body mass index (BMI) measurements. For each scenario, the student is tasked with identifying the sample size (N), calculating the sample mean, and determining the standard error of M. The solutions demonstrate the application of statistical formulas, including the formula for standard error which is the population standard deviation divided by the square root of the sample size. The assignment offers a practical application of statistical concepts, providing a step-by-step guide to solving probability problems related to sample means and standard error calculations.

Sample Means Assignment
To calculate probability problems, we must obtain values associated with the normal curve. To
help, the Population Standard Deviation value is provided for you so that you can then use that
value to calculate the Standard Error of M, or the average distance of all Sample Means from the
Mean of the Sample Means.
1. Individuals participating in a new treatment filled out a form generating program
satisfaction scores compared to other treatment group scores across the nation.
A sample from 10 different facilities is provided below.
26, 26, 23, 22, 22, 23, 14, 13, 24, 25
a) What is the N value for this sample?‘’
The value of N for this sample is 10“”
b) Calculate the mean of this sample:
Mean = Sum of all observations / total observations
= (26 +26 +23 +22 +22 +23 +14 +13 +24 +25) /10
= 218/10
= 21.8
c) Given that the Population Standard Deviation is 4.37721, calculate the
standard error of M. (The standard error of M is the standard deviation of the
distribution of sample means. You can calculate the standard error by using the
population standard deviation value and the sample size.)
Answer: Standard error = population standard deviation / sqrt (total number of sample)
= 4.3721/ sqrt (10)
= 1.38
2. An evaluation was done on the number of times visitations were made per month to high
profile children entering the foster care system. A sample was taken from data in 12 cities.
4, 3, 4, 6, 5, 4, 7, 6, 8, 5, 7, 7
a) What is the N value for this sample?‘’
The value of N for this sample is 12
b) Calculate the mean of this sample:
Sample mean = Sum of all observations / total number of sample
= (4+3+4+6+ 5+4+7+6+8+5+7+7)/12
= 66/12
= 5.5
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c) Given that the population Standard Deviation value is 1.5, calculate the
standard error of M:
Standard error = population standard deviation / sqrt (total number of
sample)
= 1.5/ sqrt (12)
= 0.43
3. As a part of the National Heath Examination, the body mass index (BMI) is
measured for a random sample for women. These values are listed below.
19.6, 23.8, 19.6, 29.1, 25.2, 21.4, 22.0, 27.5, 33.5, 20.6, 29.9,
17.7, 24.0, 28.9, 37.7
a) What is the N value for this sample?‘’
The value of N that is the total number of sample is 15
b) Compute the mean of this sample:
Sample mean = Sum of all observations / total number of sample
= (19.6 + 23.8 +19.6+29.1+
25.2+21.4+22.0+27.5+33.5+20.6+29.9+17.7+24.0+28.9+37.7) /15
= 380.5/15
= 25.36667
c) Given that the population Standard Deviation value is 5.47244, compute the
standard error of M:
Standard error = Population standard deviation / sqrt (total number of sample)
= 5.47244/ sqrt (15)
= 1.41
Syllabus Page 2 of 2