Using the Normal Distribution and Confidence Intervals: Week 4 Project Assignment

Part 1: Using the Normal Distribution

Open the “BODY DATA” file created in the Week 1 Discussion. Use it to address the following:

Given that BMI is approximately normally distributed, present the following summary statistics for BMI of “Smokers” and “Nonsmokers” in the table below.

Smokers Nonsmokers
Mean
Standard deviation
Sample size (n)

Use this table to answer the following questions based on your individual data. For each portion write a 1-sentence explanation as to how Excel was used to assist you in your computations. Note: Replace the questions (below) with your responses.

1)Find the percent of smokers expected to have a BMI of greater than 25 (overweight).
2)Find the percent of nonsmokers expected to have a BMI of less than 18.5 (underweight).
3)A normal BMI range is between 18.5 and 24.9. What percentage of smokers are expected to be within this range? What percentage of nonsmokers are expected to be within this range?
4)A researcher is interested in which BMI represents the 90th percentile (where 90% are at this BMI level or lower). What BMI score represents the 90th percentile cut-off rate?

Part 2: Creating Confidence Intervals

Using the information from Part 1 (above), calculate a 90%, 95%, and 99% confidence interval for both groups. Then, complete the following table:

Group 90% Confidence Interval 95% Confidence Interval 99% Confidence Interval
Smokers
Nonsmokers

Use this table to answer the following questions based on your individual data.
Note: Replace the questions (below) with your responses.

1.As the level of confidence increases, what happens to the width of the confidence interval? Does it increase or decrease? Explain one reason why this would happen.
2.Using the 95% confidence interval, compare the BMI of smokers versus nonsmokers. Write a 2- to 3-sentence paragraph explaining if these intervals overlap or not. What does the comparison indicate regarding the differences in BMI between the two groups?
3.Explain, in 1–2 sentences, one situation in which you (as a researcher) may choose a 99% confidence interval? A 90% interval? Fully justify your choice.

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