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

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.

## Date: June 25, 2023

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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)

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?

## Sheet1

 AGE Smoker PULSE HDL LDL WEIGHT HEIGHT BMI Region SYSTOLIC BMI SMOKERS BMI NONSMOKERS 68 0 90 95 113 45.2 151.6 19.7 4 132 28.1 19.7 51 0 94 71 98 150.4 159.7 59.0 2 120 37.0 59.0 18 0 68 62 97 71.5 158.4 28.5 2 120 36.5 28.5 18 0 90 66 76 74.0 173.6 24.6 3 106 23.1 24.6 20 0 82 78 140 64.0 160.1 25.0 2 110 20.2 25.0 45 0 80 45 112 92.8 164.8 34.2 1 146 29.6 34.2 51 0 74 47 112 85.9 172.1 29.0 4 128 24.9 29.0 63 0 56 52 121 105.5 153.2 45.0 2 156 19.9 45.0 80 0 100 65 120 43.3 134.5 23.9 1 122 25.8 23.9 59 0 74 63 119 114.9 169.1 40.2 3 124 26.0 40.2 33 0 76 45 111 89.1 160.2 34.7 1 108 33.7 34.7 60 0 76 86 95 58.5 157.8 23.5 2 136 23.4 23.5 38 0 86 49 85 57.2 166.3 20.7 4 112 32.7 20.7 68 0 74 57 135 81.4 158.4 32.4 1 136 26.8 32.4 21 0 66 63 146 95.6 177.8 30.2 3 112 18.1 30.2 37 0 62 65 148 86.5 152.4 37.2 3 110 21.3 37.2 69 0 78 47 96 79.1 164.1 29.4 3 142 23.9 29.4 46 0 68 56 143 68.4 160.6 26.5 4 112 25.2 26.5 41 0 62 46 75 85.7 167.7 30.5 4 102 22.8 30.5 80 0 62 62 104 50.4 158.8 20.0 1 130 29.7 20.0 41 0 74 61 180 72.1 156.5 29.4 2 98 31.2 29.4 68 0 104 68 99 77.2 157.6 31.1 3 140 44.2 31.1 42 0 54 66 76 83.3 169.7 28.9 2 126 29.3 28.9 64 0 74 61 121 88.6 155.0 36.9 2 120 31.6 36.9 33 0 74 40 85 84.6 170.6 29.1 1 114 35.0 29.1 63 0 84 64 98 81.0 160.1 31.6 1 114 27.1 31.6 60 0 60 81 99 53.5 156.4 21.9 1 186 29.6 21.9 35 1 54 68 100 84.1 172.9 28.1 4 126 44 1 66 40 122 112.8 174.6 37.0 3 128 37 1 56 57 71 123.9 184.3 36.5 2 114 80 1 80 47 58 76.5 182.0 23.1 3 96 18 1 72 47 87 71.7 188.4 20.2 3 120 62 1 64 43 79 90.0 174.3 29.6 3 136 41 1 64 63 133 70.6 168.5 24.9 2 106 36 1 96 97 251 64.8 180.3 19.9 2 114 80 1 58 34 69 76.6 172.2 25.8 1 136 55 1 66 63 63 93.7 189.7 26.0 2 120 32 1 58 58 140 107.4 178.5 33.7 1 122 27 1 58 39 86 74.6 178.7 23.4 2 120 62 1 68 26 122 106.0 180.0 32.7 1 142 24 1 70 62 144 84.4 177.5 26.8 2 120 19 1 84 41 69 59.6 181.3 18.1 3 108 80 1 58 74 182 63.4 172.6 21.3 3 160 27 1 78 65 158 70.4 171.5 23.9 4 118 62 1 66 44 72 69.9 166.4 25.2 1 108 35 1 86 46 126 63.7 167.1 22.8 1 120 24 1 70 47 104 90.2 174.2 29.7 3 106 28 1 54 39 123 99.4 178.6 31.2 3 128 58 1 84 36 118 127.8 170.0 44.2 1 128 18 1 72 60 84 88.3 173.5 29.3 3 128 46 1 74 42 153 94.6 173.1 31.6 3 138 45 1 64 45 167 119.8 185.1 35.0 4 116 27 1 66 49 146 78.8 170.5 27.1 3 112 69 1 62 35 84 84.4 169.0 29.6 1 120