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Created: Nov 12, 2019
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Energy/Caffeinated Beverage Consumption Inferential Statistics Report

Introduction:

Group #1 designed a survey to learn about the consumption of energy drinks and caffeinated beverages.  The population that we sampled were adults aged 21-50 years of age.  We attempted to obtain a random sample for the survey.  In our discussion group, members stated they randomly chose people they worked with, neighbors, people they met at a store, or walking on a street, for example.  These methods do not meet the true definition of a random sample, so I will have to call it a convenience sample.

We asked the following four questions:

1)      Do you drink some kind of energy or caffeinated beverage? Y/N

2)      Which one of the below beverages do you consume the most?

a. Coffee - b. Tea – c. Energy drink - d. Pop/soda - e.Other

3)      On an average day, how many of these types of beverages do you consume?

4)      On average, how many days a week do you consume these types of beverages? (1-7)

Looking at a Categorical-Variable:

The pie chart below represents data from the following question: “ Do you drink some kind of energy or caffeinated beverage?”

Result 1: Pie Chart results from question 1 on survey of energy/caffeinated beverage consumption   [Info]

The pie chart above clearly depicts that 90%,  144 out of 160 respondents, answered “yes” to the question.    16 of the 160 surveyed (10%) responded, “no."

Result 2: proportion summary confidence interval for question 1 of energy/caffeinated beverage consumption sur   [Info]

### One sample proportion summary confidence interval:

p : Proportion of successes
Method: Standard-Wald

95% confidence interval results:
ProportionCountTotalSample Prop.Std. Err.L. LimitU. Limit
p1441600.90.0237170820.853515370.94648463

Confidence Level Interpretation:  The Confidence Interval (CI) is a range of values used to estimate the true value of a population parameter.  The above Summary Results utilize a 95% CI for the yes/no question of our survey.   Our group can say that we are 95% confident that the true value of our population proportion falls between  0.854 and 0.947.  In other words, if we randomly selected many different samples of 160 and created a CI for each, 95% of them would contain the population parameter p.

Looking at a Numerical Variable

The responses to question #3 “On an average day, how many of these types of beverages do you consume?” are shown in the histogram and summary statistics below.

Result 3: Histogram of avg number of energy/caffeinated beverages consumed daily   [Info]

Result 4: Summary Stats of total surveyed in energy/caffeine beverage consumption survey   [Info]

### Summary statistics:

ColumnnMeanVarianceStd. dev.MedianRangeMinMaxQ1Q3
Average consumed daily1602.3752.46226421.569160321001013

Confidence Level Interpretation for the population mean µ:    Based on the chart in our text, I used the t-interval to calculate the CI.  Sigma σ is unknown.  Our histogram shows a slightly right-skewed graph, but our n > 30 (n=160).  These factors satisfy the requirements of using a t-distribution.

Result 5: One sample T confidence interval for question #3 in survey of energy/caffeinated beverage consumptio   [Info]

### One sample T confidence interval:

μ : Mean of variable

95% confidence interval results:
VariableSample MeanStd. Err.DFL. LimitU. Limit
Number of drinks per day2.3750.124053021592.12999582.6200042

The above Summary Results use a 95% Confidence Interval regarding the population mean µ.  Our group can say with 95% confidence that the actual value of µ falls between the limits of 2.130 and 2.620.  Another way of saying this is if we randomly select many samples of  160 adults, 21-50 years of age, and calculated the CI of each sample, 95% of them would contain the actual population mean.

Data set 1. Consumption of Energy or Caffeinated Beverages of   [Info]