Question

1. A medical researcher attempted to learn if a disease is accompanied by an increased in body temperature.  She measured the body temperature of 12 people diagnosed as having the disease and obtained the following temperatures (in degrees F):  99.3, 99.1, 100.4, 98.4, 98.2, 98.9, 99.7, 100.1, 100.7, 99.0, 98.8, 99.2.

Does the mean body temperature of these individuals differ from a hypothesized population mean of 98.6 degree F?  Use a two-tailed test and a 0.05 significance level

Step 1:

Step 2:

Step 3:

Step 4:

Additional question: Could your decision regarding the statistical hypothesis represent a Type II error?  Explain your answer.

Answer 1

SOLUTION-

1.) LET BE THE MEAN BODY TEMPERATURE OF THE INDIVIDUALS. THE HYPOTHESIS FRAMED HERE IS,

AS THE POPULATION STANDARD DEVIATION IS UNKNOWN, WE USE A ONE SAMPLE-T TEST AND ALSO USE MINITAB-16 FOR CALCULATIONS.

STEPS-

ENTER THE DATA> STAT> BASIC STATISTICS> ONE SAMPLE-T> SELECT THE DATA> SET THE HYPOTHESIZED MEAN AS 98.6> UNDER 'OPTIONS', SET THE CONFIDENCE LEVEL AS 95.0 AND ALTERNATE AS 'NOT EQUAL'> OK

OBSERVATIONS-

THE TEST STATISTIC IS T=3.22 AND THE CORRESPONDING P-VALUE IS 0.008

AS P-VALUE<0.05, WE REJECT THE NULL. SO THE MEAN TEMPERATURE DIFFERS FROM 98.6' F.

2.) TYPE II ERROR REPRESENTS THE FAILURE TO REJECT THE FALSE NULL HYPOTHESIS.

NOW IF THE VALUE OF THE NULL HYPOTHESIS IS MISTAKEN, THE PROCEDURE CAN INCURR A TYPE II ERROR SCENARIO.

****IN CASE OF DOUBT, COMMENT BELOW. ALSO LIKE THE SOLUTION IF POSSIBLE.