Hot Dog Calories - Poultry versus Beef

Posted: November 11, 2015
Goal: Determine if there is a statistically significant difference in the mean number of calories between two types of hot dogs.
Purpose: This activity models the concept behind the t-test for comparing two means.
Data set retrieved from: DASL [meat type and sodium were deleted]


You Tube Video - Posted 6-5-17

Screen Shot 2015-11-11 at 8.27.46 AM.png

Step One
Graph the number of calories split by type (parallel dot plot) and show the means.
Hypotheses
Ho: The mean number of calories for the 20 brands of beef hot dogs is the same as the mean for the 17 brands of poultry hot dogs.
Ha: The mean number of calories for the 20 brands of beef hot dogs is greater than the mean for the 17 brands of poultry hot dogs.

Step Two
Snap the ruler tool to each of the means. The alternate hypothesis states that the average number of calories is significantly higher for the beef hot dogs, because the difference is in a positive direction.
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Step Three
Pull down a case table and create two new variables as shown below.
Use the Options menu to show the formulas in the case table.
Use the tab key to move within the “if” command.
Use double quotes to indicate that A and B are text entries.
Screen Shot 2015-11-11 at 8.37.07 AM.png
Step Four
Graph Calories split by Group.
Use the ruler tool to find the difference of the means. Measure from the smaller group to the larger group.

Click on the History tool and then click on the difference of the means [there will be a light grey box around the number]. In the example shown below, the difference between the means is 5.1 calories.

Immediately after clicking on the difference, a new case table appears. The history case table will capture results of repeated random assignments of 17 and 20.
Screen Shot 2015-11-11 at 8.41.36 AM.png

Step Five
The history table will contain one case. Delete this case [Options - delete all history cases] and change the collect value to 100. Collect a total of 100 simulations.
Screen Shot 2015-11-11 at 8.44.42 AM.png
Step Six
Graph the Diff_Calories attribute on a new plot. Place a vertical reference line at 38.1 diff calories. Note that none of the 100 differences fall above 38.1 calories.
Screen Shot 2015-11-11 at 8.49.05 AM.png

Step Seven
In order to graph a new set of 100 trials, open the options menu and select Delete All History Cases.

Collect 100 new cases (differences between the means) and note the number of differences that fall above the "cut score" of 38.1 calories.
Screen Shot 2015-11-11 at 8.51.28 AM.png

Step Eight
To be statistically significant we expect to find, on average, fewer then five cases (differences of the mean number of seeds) above the cut score. This is based on an alpha level of 0.05.
After repeating the simulation 6 times (100 in each), none of the differences fell above 38.1. After turning off the animation [Object | Inspect Collection], I collected 10,000 samples. The largest positive difference is 34.9 calories.
Screen Shot 2015-11-11 at 8.57.20 AM.png
Based on this information, I decided to reject the null hypothesis. There is enough evidence that, when left to chance, the mean number of calories in the 20 brands of beef hot dogs is greater than the number of calories in the 17 brands of poultry hot dogs.

Summary
This curve should look familiar. The data is normally distributed and divided into two regions. The percentage of data above 38.1 is 0%, which is less than the 5% alpha value commonly used in hypothesis testing.

The completed file is shared below.


FYI - Fathom results
Calories_pvalue.png