Question

A study was conducted to determine if the salaries of librarians from two neighboring states were equal. A sample of 100 librarians from each state was randomly selected. The mean from the first state was $29,800 with a standard deviation of $2,200. The mean from the second state was $31,400 with a standard deviation of $2,150. Test the hypothesis that there is no difference in the salaries from both states at the 0.05 significance level.

1. Determine the test statistic. Round to four decimal places.
   t=
   
2. Find the pp-value. Round to 4 decimals.
   p-value =

Answer 1

SOLUTION-

LET BE THE MEAN SALARY FOR FIRST STATE AND BE THE MEAN SALARY FOR SECOND STATE. WE WANT TO TEST IF THE TWO MEANS ARE EQUAL. THE HYPOTHESIS IS,

AS THE SAMPLES ARE INDEPENDENT, WE PERFORM A TWO SAMPLE-T TEST AT 0.05 SIGNIFICANCE LEVEL IN MINITAB-16

STEPS- STAT> BASIC STATISTICS> TWO SAMPLE-T> ENTER THE SUMMARIZED DATA> UNDER 'OPTIONS', SET THE CONFIDENCE LEVEL AS 95.0 AND ALTERNATE AS 'NOT EQUAL'> OK.

1.) THE TEST STATISTIC IS T= -5.20

2.) THE P-VALUE IS 0.000

AS P-VALUE<0.05, REJECT THE NULL HYPOTHESIS.

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