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Created: Mar 23, 2017
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M5A2 Inferential Statistics Report
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My group and I designed a survey to explore an individual's perspective of the New Year’s Weight Loss Resolution.  The focus of our survey was to determine if there is a relationship between a medical recommendation versus personal goal in losing weight for the New Year and how it may affect the individual's motivation level in pursuing this goal.  The population that was sampled were adults, with a New Year's Resolution to lose weight.  Our data was collected by asking individuals “ Do you have a New Year’s Resolution to lose weight?”, if they answered “Yes” to the question they were given a survey. Using this method we first divided the population area into two sections, those with a New Year’s Resolution to lose weight, and those who did not have a New Year’s Resolution to lose weight. With this method we used all members from the sample cluster who had a New Year’s Resolution to lose weight. We also poled through Facebook and StatCrunch.  Therefore, our survey is composed of cluster sampling and convenience sampling with voluntary responses.  


We asked the following questions:

  1. What is your personal goal weight that would make you happy? ____ (Pounds)

  2. What is your current weight? ____ (Pounds)

  3. Has a Healthcare Provider recommended to you the need to lose weight to control an actual or potential medical problem? Yes/No

  4. How motivated are you to reach your New Year’s weight loss goal? Please choose one of the following:

(5) Very Motivated

(4) Motivated

(3) Somewhat Motivated

(2) Unmotivated

(0-1) Very unmotivated

Looking at Categorical-Variables

The responses to the question “ Has a Healthcare Provider recommended to you the need to lose weight to control an actual or potential medical problem?” are shown in the following pie chart.

Result 1: Pie Chart Responses to Healthcare Provider Recommendation   [Info]
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As shown, in the pie chart, we are able to determine that 74 out of the 101, or approximately 73%, of the participants were recommended by their Healthcare Provider to loss weight and 27, or approximately 27%, of the 101 participants were not given recommendations.  

Result 2: 95% Confidence Interval Results   [Info]
One sample proportion confidence interval:
p : Proportion of successes
Method: Standard-Wald

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


Listed above is a 95% Confidence Interval for the participants who answered “Yes” to the question, “ Has a Healthcare Provider recommended to you the need to lose weight to control an actual or potential medical problem?” To understand a confidence interval,  we must know that the interval is a range of values used to determine the specific probability that the true population parameter would lie within.  To further explain, given our sample size n=101, if we were to chose many different sample sizes of n=101,  approximately 95% of those samples should contain the true proportion of the population.  In interpreting the summary above we are 95% confident the true proportion of our population who would answer “Yes” to the question is within 0.181 to 0.354.  The error term is E= (0.354-0.267)/2 = 0.087/2 = 0.0435 = 0.44 (margin of error)

Looking at Numerical Variable

The responses to the question “ What is your current weight?” are shown in the histogram and summary statistics below

Result 3: Histogram of Participant's Current Weight   [Info]
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Result 4: Summary Stats of Participant's Current Weight   [Info]
Summary statistics:
ColumnnMeanVarianceStd. dev.Std. err.MedianRangeMinMaxQ1Q3
Current Weight101182.371291770.393342.0760414.1867226180212118330147205

A 95% confidence interval for population mean is shown below

Result 5: One Sample T Statistics of Current Weight   [Info]
One sample T confidence interval:
μ : Mean of variable

95% confidence interval results:
VariableSample MeanStd. Err.DFL. LimitU. Limit
Current Weight182.371294.1867226100174.06495190.67763

In order to understand the confidence interval illustrated above, if we were to select many different sample of n=101, approximately 95% of the samples would result in confidence intervals that would contain the true population mean.  We can then state that we are 95% confident that the confidence interval of the sample contains the true population mean.  Concluding that we are confident that, within our population, 95% have an average current weight of 174-191 pounds.  

Since the standard deviation of the population is unknown, t-distribution was used to determine our data.  


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