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Owner: julesk75
Created: Jul 10, 2019
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Inferential Statistics Report- Exercise
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I. Introduction:

     a. My group and I designed a survey to find out if our friends and acquaintances exercised, and whether or not they were concerned about their exercise habits. This was not a random survey, as we used Facebook, email and face to face contacts to get our results. This was a voluntary survey, and not everyone asked responded.

     b. We asked the following questions:

  1. Do you currently exercise?  Yes or No
  2. How old are you? ____ years
  3. How many hours of exercise a week do you think an average person requires to be healthy? _____hours
  4. How concerned are you with your level of activity? Select one: Highly concerned, Moderately concerned, Not at all concerned?

II. Looking at a Categorical Variable


     a. The responses to the question " Do you currently exercise?" are shown in the pie chart below.

Result 1: Pie Chart Responses to Currently Exercise?

 

Result 1: Pie Chart With Data- final   [Info]
Right click to copy

 

From the pie chart above we can see that 54 of the 100 people we polled (54%) said that they do currently exercise.   Forty-six (46%) do not currently exercise.

     b.

Result 2: A sample proportion with summary

95% confidence interval results:

 p: proportion of successes for population

Method: Standard-Wald

 

Result 2: One sample proportion confidence interval   [Info]

One sample proportion confidence interval:


Outcomes in : Exercise?
Success : Yes
p : Proportion of successes
Method: Standard-Wald

95% confidence interval results:
VariableCountTotalSample Prop.Std. Err.L. LimitU. Limit
Exercise?541000.540.0498397430.44231590.6376841

 

Interpretation of the confidence interval: Above is the 95% confidence interval results for the proportion of the population that would answer "yes" to the question "Do you currently exercise?". A 95% confidence interval means that if you select multipe different samples of size n=100, approximately 95% would result in confidence intervals that contain the true proportion p. The above results can be interpreted as saing we are 95% confident that our confidence interval contains the true proportion, and we are 95% confident the true proportion of our population would answer yes to this question is between 0.442 to 0.638.

The error term E=(.638-.054)/2=0.083/2= 0.042 (margin of error).

 

III. Looking at a Numerical Variable

a.

 The responses to the question "How many hours of exercise a week do you think an average person requires to be healthy?" are shown in the histogram and summary statistics below. 

Result 3:

 

Result 3: Histogram- hours   [Info]
Right click to copy

Result 4: Summary Statistics for Hours per Week Required

 

Result 4: Summary Stats-hours   [Info]

Summary statistics:


ColumnnMeanVarianceStd. dev.Std. err.MedianRangeMinMaxQ1Q3
Hours1006.4324.186974.9180250.491802552402437

 

b. 

A 95% confidence interval for the population mean is shown below.

 

Result 5: One sample T confidence interval-hours   [Info]

One sample T confidence interval:


μ : Mean of variable

95% confidence interval results:
VariableSample MeanStd. Err.DFL. LimitU. Limit
Hours6.430.4918025995.45415717.4058429

Interpretation of the confidence interval: a 95% confidence interval means that if we selected many diffferent sample s of size n=100, approximately 95% of these would result in confidence ntervals that contain the true proportion mean u. We can interpret the above reults by saying we are 95% confident that our confidence interval contains the true proportion mean.  So, we are 95% confident that within our population, the average person thinks we need between 5.5 and 7.4 hours per week.

The t-distribution was used becasue the sample size is more than 30 and the population standard deviation is not known.

 

 

 

 

Interpretation of the confidence interval: 

HTML link:
<A href="https://www.statcrunch.com/5.0/viewreport.php?reportid=88303">Inferential Statistics Report- Exercise</A>

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