Problem 91

Given information

A powder diet is tested on  people, and a liquid diet is tested on  different people. Of interest is whether the liquid diet yields a higher mean weight loss than the powder diet. The powder diet group had a mean weight loss of  pounds with a standard deviation of  pounds. The liquid diet group had a mean weight loss of    pounds with a standard deviation of   pounds.

Step-by-step explanation

 

Now, consider the following observations:

The null hypothesis is defined as follows:

     

The alternative hypothesis is stated as follows:

    

The random variable is the difference in mean weight loss between the liquid and powder diets.

Student’s t distribution.

Press STAT and to locate test static.

TESTS must be selected twice.

To enter the stat list editor, press STAT followed by .

After ENTER all of the values, look at the OUTPUT below.

Test statistic .  

The output yields a -value of .

Drawing a representation of the situation using the information from the last exercise.

The horizontal axis should be clearly labeled and scaled, and the region(s) matching the should be shaded on the graph.

    

  

     

   Decision: Null hypothesis is rejected.

   

    Conclusion: At the  significance level, there is insufficient evidence to say that the liquid diet is more effective than the powder diet in terms of weight loss.

There is not enough proof to conclude that the liquid diet yields more weight loss than the powder diet