A group of psychiatrists want to investigate if there is anydifference in depression levels (measured on a scale from [0=not atall depressed] to [100=severely depressed]) in patients who havebeen treated for depression by being told to regularly exerciseversus those who were given an oral medication, Contentica, totreat depression.

The researchers selected a sample of 15 patients who were toldto regularly exercise and found that their mean depression levelwas a score of 48 with a standard deviation of 9.

The researchers also selected a sample of 14 patients who weregiven the medication Contentica and found that their meandepression level was a score of 54 with a standard deviation of10.

Conduct an appropriate two-tailed hypothesis test (twoindependent samples t-test) on whether or not patients whoregularly exercise have a differentdepressionlevel than those who are prescribed the medication Contenticausing an alpha (?) level of 0.01.

You will use the information above to complete the questionparts below for a two independent samples t-test.

Part A: Which of the following represents theappropriate null hypothesis(H₀),given this research question of interest?

PART A ANSWER: H₀:                   

       [ Select ]                     ["?1 = 15", "?1 - ?2 = 0", "?1 - ?2 =54", "?1 - ?2 = 48", "?1 - ?2 ? 48"]      

Part B: Which of the following represents theappropriate alternative hypothesis(H₁), given this research question ofinterest?

PART B ANSWER: H₁:                   

       [ Select ]                     ["?1 - ?2 ? 48", "?1 - ?2 ? 14", "?1 - ?2? 54", "?1 ? 15", "?1 - ?2 ? 0"]      

Part C: What is the degrees of freedom(df)associated with your test?

PART C ANSWER:                 

      [ Select ]                     ["21", "45", "10", "27", "54"]     

Part D: Which of the following represents theappropriate critical value(s), testing at analpha level (?) of 0.01?

PART D ANSWER:                      

    [ Select ]                     ["-2.892 and 2.892", "-2.771 and 2.771", "-2.312 and2.312", "-1.251 and 1.251", "3.85"]      

Part E: What is the pooledvariance(s²_p) associated with yourtest? (rounded to the nearest hundredth)

PART E ANSWER:                 

      [ Select ]                     ["45.12", "315.81", "90.15", "76.43", "12.86"]     

Part F: What is the estimated standarderror of x?₁ - x?₂ associated withyour test? (rounded to the nearest hundredth)

PART F ANSWER:                    

      [ Select ]                     ["3.53", "4.16", "7.89", "2.98", "1.05"]     

Part G: What is thet-statistic associated with your test?(rounded to the nearest hundredth)

PART G ANSWER:                      

[ Select ]                      ["1.21","5.47", "3.96", "2.85", "-1.70"]      

Part H: Given your test results, what is yourdecision about the null hypothesis?

PART H ANSWER:                       

   [ Select ]                      ["Rejectthe null", "Fail to reject (i.e., retain) the null"]     

Part I: The best interpretation of theappropriate decision regarding the null hypothesis would be: "Basedon our study, we                           [ Select ]                      ["have","do NOT have"]         enoughevidence to conclude that patients who regularly exercise do appearto have a different depression level than those who are prescribedthe medication Contentica."

Part J: Which of the below represents a99% confidence interval for the difference betweenthe unknown population mean cholesterol levels of people on the newexercise regimen and people on the new medication?

PART J ANSWER:                    

       [ Select ]                     ["[-18.28 to -3.16]", "[-15.78 to 3.78]","[-7.39 to 1.05]", "[-12.81 to 10.45]", "[3.45 to 9.82]"]