Mathematics – Statistics Week 4_Assignment_USING THE NORMAL DISTRIBUTION AND CONFIDENCE INTERVALS

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USING THE NORMAL DISTRIBUTION AND CONFIDENCE INTERVALS

Instructions:

  1. This Assignment will make use of the data set created in Week 1 – See attached excel document.
  2. Use the attached word document to complete this week assignment.

 

Part 1: Using the Normal Distribution

Given that BMI is approximately normally distributed, present the following summary statistics for BMI of smokers and nonsmokers in the table below.

Smokers Non-smokers
Mean
Standard Deviation
Sample size (n)

Use this table to answer the following questions based on your individual data. Compute probabilities based on the normal distribution. For each portion write a 1-sentence explanation as to how Excel was used to assist you in your computations.

  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
Non-smokers

Use this table to answer the following questions based on your individual data.

  1. As the level of confidence increases, what happens to the width of the confidence interval? Does it increase or decrease? Explain one (1) 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.