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.
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 weight: 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 α = .
a. Find the sample mean and sample standard deviation of the height. Denote them as x¯ and sx respectively.
b. Find the sample mean and sample standard deviation of the shoe sizes. Denote them as y¯ and sy respectively.
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 α 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?
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