(Solved): 1. To study about the correlation between height and shoe size, you need to collect a sample ...
1. To study about the correlation between height and shoe size,
you need to collect a sample of nine (9) people
using a Systematic Sampling method.
a. 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?
b. Collect the sample and record the data. Use a single unit for
height. Do not use a mixed unit like feet and
inches.
Person 1 Person 2 Person 3 Person 4 Person 5 Person 6 Person 7
Person 8 Person 9
Height
Shoe Size
2. (CLO 1) Construct a confidence interval to estimate the mean
height and the mean shoe size: you must complete
the following questions by first choosing a Confidence Level. You
may choose from the familiar 90%,95%, or
99% level of confidence.
Denote this by choosing ? = .
a. Find the sample mean and sample standard deviation of the
height. Denote them as ?x and sxrespectively.
b. Find the sample mean and sample standard deviation of the shoe
sizes. Denote them as ?y and syrespectively.
c. Construct and interpret a confidence interval to estimate the
mean height of the population. You must
first write the formula for the confidence interval and then
substitute your appropriate numbers.
d. Construct and interpret a confidence interval to estimate the
mean shoe size of the population. You must
first write the formula for the confidence interval and then
substitute your appropriate numbers.
3. (CLO 2) Test a claim that the mean height of your population
is different from 64 inches. Use the appropriate
significance level ? you fixed earlier.
a. State the initial and alternative hypothesis.
b. Find the test statistic and the P-value. You must first write
the formula for the test statistic and then
substitute your appropriate numbers.
c. Draw a conclusion in context of the situation. Your conclusion
should include both the formal language as
well as an informal explanation.
4. (CLO 3) Find a correlation between height and shoe size.
a. Create a scatterplot of the data. Height is x-axis and Shoe size
is y-axis. Attach your scatterplot to the end
of this document.
b. Find the linear correlation coefficient. What does this tell you
about your data?
c. Write the equation of the regression line and use it to predict
the shoe size of a person that is 68 inches tall.
5. 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?