Exhale Data Analysis Project Math 1040Autumn Beckstead

Summer 2014

Part I:The data set that I choose is the Exhale study. In this data set they are comparing the forced expiratory volume in liters between people of different ages, sex, height, and whether they smoke or not. Throughout the project different charts and formulas will be used to come to a hypothesis about the data.

Part II:Pie Chart & Pareto Chart for entire Gender Population:In a population of 654 subjects being tested, the frequency of female subjects in the entire study is 318, which correspond to 48.62% of the sample, and 336 male subjects that correspond to 51.38% of the sample.

Pie Chart & Pareto Chart for Simple Random Sampling:To obtain simple random data first I determined the sample size should be 50. Then I used the stat crunch sample generator to compute the data.

Pie Chart & Pareto Chart for Systematic Random Sampling:To obtain simple random data first I determined the sample size should be 50. Then I used excel and selected every 12th number.

Comparing Results:When comparing the results with the entire population I found that the simple random sample was the closest to the entire population. The systematic sample seemed to be more skewed away from the results of the entire population.

Part III:Mean, Standard Deviation, Five-Number Summary, Frequency Histogram, and Box Plot for Entire Height Population.

Column Mean Std. dev.Height - inches

61.143578

5.7035128

Five Number SummaryColumn Mi

nQ1

Median

Q3 Max

Height - inches

46 57 61.5 65.5

74

Mean, Standard Deviation, Five-Number Summary, Frequency Histogram, and Box Plot for Random Sampling of Height PopulationTo obtain simple random data first I determined the sample size should be 50. Then I used the stat crunch sample generator to compute the data

Column Mean

Std. dev.

Height Simple Random Sample

61.11

4.708102

Five Number SummaryColumn Mi

nQ1

Median

Q3

Max

Height Simple Random Sample

51 58 61.5 64 70

Mean, Standard Deviation, Five-Number Summary, Frequency Histogram, and Box Plot for Systematic Sampling of Height Population.To obtain simple random data first I determined the sample size should be 50. Then I used excel and selected every 12th number.

Column Mean

Std. dev.

Height Systematic Sample

59.6 5.4398379

Five Number SummaryColumn Mi

nQ1

Median

Q3

Max

Height Systematic Sample

48 55 60.75 63 71

Comparing Results:When comparing the results to the entire population it seems that the systematic sample frequency histogram looks very similar to the entire population whereas the simple random sample box plot looks most similar to the entire height population box plot.

Part IV:Simple Random Sample Categorical Variable (Sample 1): Confidence Interval

There is a 95% confidence that the sample proportion is between 0.38 and 0.66.

Systematic Sample Categorical Variable (Sample 2): Confidence Interval

There is a 95% confidence that the sample proportion is between 0.26 and .54.Simple Random Sample Quantitative Variable (Sample 3): Confidence Interval for Mean:

There is a 95% confidence that the sample mean is between 59.77 and 62.45.

Systematic Sample Quantitative Variable (Sample 4): Confidence Interval for Mean:

There is a 95% confidence that the sample mean is between 58.05 and 61.15Simple Random Sample (Sample 3): Confidence Interval for Standard Deviation:

There is a 95% confidence that the sample standard deviation is between 3.13 and 6.29.

Systematic Sample (Sample 4): Confidence Interval for Standard Deviation:

There is a 95% confidence that the sample standard deviation is between 3.86 and 7.02.

Interpreting the Data: Confidence intervals are what we use to estimate the true value of the population parameter. If use several different samples all with the same confidence level than that percentage of the samples would contain the population parameter. Therefore from the samples taken you can conclude that it did capture the population parameter within the samples.

Simple Random Sample Categorical Variable (Sample 1): Hypothesis Test

We fail to reject the null hypothesis because there is enough evidence to support that the true population proportion is 48.62%.

Systematic Sample Categorical Variable (Sample 2): Hypothesis Test

We fail to reject the null hypothesis because there is enough evidence to support that the true population proportion is 48.62%.

Simple Random Sample Quantitative Variable (Sample 3): Hypothesis Test

We fail to reject the null hypothesis because there is enough evidence to support that the true population mean is 61.14%.

Systematic Sample Quantitative Variable (Sample 4): Hypothesis Test

We reject the null hypothesis because there is not enough evidence to support that the true population mean is 61.14%.