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Created: Jul 27, 2013
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Inferential Statistics Report on Diet and Exercise

Inferential Statistics Report

Introduction:

(a)

The purpose of the Health and Diet survey was to see how diet and exercise fit into the persons’ surveyed life.  This was a convenience sample of adults aged 20 to 60 through Facebook, e-mails and coworkers

(b)

1.  How many days a week do you exercise?

2.  How many soft drinks a week do you drink?

3.  In the past 6 months, have you lost weight?     Yes/No

4.  Of these healthy diet choices, which one do you have the most difficulty including in your diet?

Vegetables/Fruits/Whole grains/Lean meats (Protein)/Dairy

Looking at a Categorical Variable:

(a)

Our question:  In the past 6 months, have you lost weight?  The pie chart that follows shows the results:

Result 1: Weight loss in 6 months   [Info]

95% confidence interval results:
Outcomes in : gain/lbs/6month
Success : Yes
p : proportion of successes
Method: Standard-Wald

 Variable Count Total Sample Prop. Std. Err. L. Limit U. Limit gain/lbs/6month 80 153 0.52287585 0.040380277 0.44373193 0.6020197

In interpreting the above results, we can say with 95% confidence that the interval of 0.444 to 0.602 does have the true value of the population proportion with the probability being 0.5.

Looking at a Numerical Variable:

The numerical variable in that was analyzed in the last section, our question is, In the last 6 months, have you lost weight? Yes/no

(a)

Below is a histogram comparing the number of days a week a participant exercised with whether they’ve lost weight in the last 6 months.  Even though the label says gain/lbs/6mos, the question stated was “Have you lost weight in the last 6 months? Yes/no?”  So the yes answer means weight lost (not gained) and no means no weight loss.

(histogram)

Result 2: Histogram of weight loss with days exercising   [Info]

Summary statistics for days/exercise:
Group by: gain/lbs/6month

 gain/lbs/6month n Mean Variance Std. Dev. Std. Err. Median Range Min Max Q1 Q3 No 73 3.0547945 4.219178 2.0540638 0.24040999 3 7 0 7 2 5 Yes 80 1.9625 3.2011075 1.789164 0.2000346 2 6 0 6 0 3

(b)

(Z stats)

95% confidence interval results:
Group by: gain/lbs/6month
μ : mean of days/exercise
Std. Dev. not specified.

 gain/lbs/6month n Sample Mean Std. Err. L. Limit U. Limit No 73 3.0547945 0.24040999 2.5835996 3.5259895 Yes 80 1.9625 0.2000346 1.5704393 2.3545606

For this data, I used the z-statistic with our sample population being >30.

Since our sample population is >30 we can assume a normal distribution and use the z-statistic.

With this result, we interpret as being 95% confident that 1.570 and 2.354 days does contain the true value of µ.