Sodium

=**Hot Dog Sodium - Poultry versus Beef Hot Dogs**= Posted: November 15, 2015 Goal: Determine if there is a statistically significant difference in the mean grams of sodium 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 [the meat hot dog type was deleted]

You Tube Video - Posted June 5, 2017

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

Snap the ruler tool to each of the means. The alternate hypothesis states that the average grams of sodium is significantly higher for the poultry hot dogs, because the difference is in a positive direction.
 * Step Two**

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.
 * Step Three**

Graph Sodium split by Group. Use the ruler tool to find the difference of the means. Measure from the larger group to the smaller group.
 * Step Four**

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 40 grams of sodium.

Immediately after clicking on the difference, a new case table appears. The history case table will capture results of repeated random assignments of size 17 and 20.

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.
 * Step Five**

Graph the Diff_Sodium attribute on a new plot. Place a vertical reference line at 58. Note that 5 of the 100 differences fall above +58 grams of sodium. In order to graph a new set of 100 trials, open the options menu and select Delete All History Cases.
 * Step Six**
 * Step Seven**

Collect 100 new cases (differences between the means) and note the number of differences that fall above the "cut score" of 58 grams of sodium. The next two simulations of 100 trials each yielded 4 and then 3 differences above 58 grams, respectively.

To be statistically significant we expect to find, on average, fewer than five cases of 100 (or 5%) above the cut score for a one tailed test. This is based on an alpha level of 0.05. After repeating the simulation a number of times (100 in each), five of the eight simulations had 5 or more differences that fell above 58 [5,4,3,5,2,8,9,3]. The results are too close to make a decision.
 * Step Eight**

After **turning off** the animation [Object | Inspect Collection], I collected 1,000 samples and 3% fell above the cut score. == The last simulation shows 5,000 samples and 4% fell above the cut score. Based on this information, I decided to reject the null hypothesis. //There is enough evidence that, when left to chance, the mean number of grams of sodium in the 17 brands of poultry hot dogs is greater than the number of grams of sodium in the 20 brands of beef hot dogs.// This curve should look familiar. The data is normally distributed and divided into two regions. The percentage of data above 58 grams is approximately 4%, which is less than the 5% alpha value commonly used in hypothesis testing. The completed file is shared below.
 * Summary**


 * FYI - Fathom results**