The Relationship Between Height and Weight

To study about the relationship between height and the weight, you need to collect a sample of nine (9) people using a systematic sampling method. 

What is the population of people? Where and how are you going to collect your sample? Does your sample accurately represent your population? Why or why not? 

To study the relationship between height and weight, sample data were collected using a systematic method. The study population was local football players. Nine local teams were systematically selected from nine states. One player was then randomly selected from each team. The height and weight of the nine players that were selected were then measured and recorded. However, the sample selected does not accurately represent the actual population. This is because the sample is very small, and the size of the population cannot be reasonably approximated. In addition, some local teams were ignored because they were not readily accessible. 

Collect the sample and record the data. 

	Person 1	Person 2	Person 3	Person 4	Person 5	Person 6	Person 7	Person 8	Person 9
Height (Inches)	68.9	68.9	70.1	70.9	72	74	72.8	67	67
Weight lbs)	141	174	172	179	163	157	176	143	147

(CLO 1) Construct a confidence interval to estimate the mean height and the mean weight by completing the following: 

Find the sample mean and the sample standard deviation of the height. 

	Height	Height -X	(Height-X)^2
Person 1	68.9	-1.2778	1.6327
Person 2	68.9	-1.2778	1.6327
Person 3	70.1	-0.0778	0.0060
Person 4	70.9	0.7222	0.5216
Person 5	72	1.8222	3.3205
Person 6	74	3.8222	14.6094
Person 7	72.8	2.6222	6.8760
Person 8	67	-3.1778	10.0983
Person 9	67	-3.1778	10.0983
Mean	70.1778
Total			48.7956

Alternative, the sample mean and the sample standard deviation of the height can be calculated using excel functions. 

	Height
Person 1	68.9
Person 2	68.9
Person 3	70.1
Person 4	70.9
Person 5	72
Person 6	74
Person 7	72.8
Person 8	67
Person 9	67
Mean	70.1778
Standard Deviation	2.3285

Find the sample mean and the sample standard deviation of the weight. 

	Height	Height -X	(Height-X)^2
Person 1	141	-20.3333	413.4444
Person 2	174	12.6667	160.4444
Person 3	172	10.6667	113.7778
Person 4	179	17.6667	312.1111
Person 5	163	1.6667	2.7778
Person 6	157	-4.3333	18.7778
Person 7	176	14.6667	215.1111
Person 8	143	-18.3333	336.1111
Person 9	147	-14.3333	205.4444
Mean	161.3333
Total			1778

Alternatively, the sample mean and standard deviation of the weight can be calculated using excel functions. 

	Weight
Person 1	141
Person 2	174
Person 3	172
Person 4	179
Person 5	163
Person 6	157
Person 7	176
Person 8	143
Person 9	147
Mean	161.3333
Standard Deviation	14.05545

Construct and interpret a confidence interval to estimate the mean height. 

Let us construct a 95% confidence interval (CI). 

Construct and interpret a confidence interval to estimate the mean weight. 

(CLO 2) Test a claim that the mean height of people you know is not equal to 64 inches using the p-value method or the traditional method by completing the following: 

State H0 and H1. 

Find the p-value or critical value(s). 

Let set the significant level at 0.05. 

Where, 

Using online calculators, 

Draw a conclusion in context of the situation. 

Therefore, the null hypothesis is rejected. 

(CLO 3) Create a scatterplot with the height on the x-axis and the weight on the y-axis. Find the correlation coefficient between the height and the weight. What does the correlation coefficient tell you about your data? Construct the equation of the regression line and use it to predict the weight of a person who is 68 inches tall. 

Correlation	0.51084
Slope	3.08361
Intercept	-55.068

The correlation coefficient is slightly greater than 0.5. This indicates that there is a moderate positive relationship between height and weight. From the graph, the points do not fall on the regression line. This indicates that height and weight are not linearly related. 

The equation of the regression line is: 

Write a paragraph or two about what you have learned from this process. When you read, see, or hear a statistic in the future, what skills will you apply to know whether you can trust the result? 

From this task, I have learnt a number of things. First, I have how to construct and interpret the CI. CI is about risk. CI consider the sample size and the potential variation in the population. Based on this, CI gives us an estimate of the range within which the real answers lie. Secondly, I have learned about hypothesis testing using p-values. CI and hypothesis testing give us additional information about a given population or set of values. When I read, see or hear a statistic in the future, I will apply the concepts of CI and hypothesis testing to determine if the result can be trusted. CI and hypothesis testing can help gain more insight into the metrics captured.