Statistics Homework: Sample Means, Standard Error, and Calculations

This assignment focuses on calculating sample means and the standard error of M. The problems involve calculating the mean of various samples and then determining the standard error using the provided population standard deviation and sample size. The assignment covers three different scenarios: program satisfaction scores, monthly visitations to foster care children, and body mass index (BMI) measurements for women. The solutions include step-by-step calculations for each part, demonstrating how to apply the formulas and interpret the results. The assignment is designed to help students understand how to work with sample data, population standard deviations, and the concept of standard error in statistical analysis.

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?
Answer: N= 10
b) Calculate the mean of this sample:
Answer: Mean = (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 = standard deviation / sqrt (total sample observations)
= 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?
Answer: N= 12
b) Calculate the mean of this sample:
Answer: Sample mean= (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:
Answer: standard error = standard deviation / sqrt (total sample observations)
= 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?
Answer: N= 15
b) Compute the mean of this sample:
Answer: Sample mean = (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
= 370.5/15
= 24.7
c) Given that the population Standard Deviation value is 5.47244, compute the standard
error of M:
Answer: standard error = standard deviation / sqrt (total sample observations)
= 5.47244/ sqrt (15)
= 1.41
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