Question

1. A travel agent claims the average seven-day cruise to the Caribbean is cheaper than the average seven-day cruise to Alaska. Here are the data of the average cost of seven-day cruises to the Caribbean and Alaska based on various cruise lines. Assume the significant level α=0.05.

The Caribbean :    $1099     $1057       $1121      $1068       $1185       $1100

                              Alaska :                  $1165     $1184       $1246      $1301       $1284       $1200

1. State the null hypothesis and the alternative hypothesis. Make sure you clearly indicate the parameters  for “the Caribbean” or for “Alaska”.

H0:

Ha:

2. Calculate the test statistic. Specify which test statistic you are finding (“z” or “t”).

3. Find the p-value using the appropriate table. Be sure to include any appropriate degrees of freedom.   Draw the curve showing p-value, critical value(s)(α=.05), rejection region.

4. At a significance level of 0.05, would you reject or retain the null hypothesis? Circle your response and explain why you chose this response.

            Reject Ho / Do NOT Reject Ho               Why?

5. If the significant level decreases to 0.01, do you still keep the same conclusion? Explain why.

Answer 1

SOLUTION-

A TRAVEL AGENT CLAIMS THAT THE AVERAGE SEVEN DAY CRUISE TO CARIBBEAN IS CHEAPER THAN ALASKA

A.) LET BE THE POPULATION MEAN FOR CARIBBEAN AND BE THE POPULATION MEAN FOR ALASKA.

THE APPROPRIATE HYPOTHESIS FOR THIS SCENARIO IS-

WE USE MINITAB-16 TO COMPUTE THE CALCULATIONS AND PERFORM A TWO SAMPLE-T TEST

STEPS: ENTER THE DATA IN SEPERATE COLUMNS> STAT> BASIC STATISTICS> TWO-SAMPLE T> ENTER THE SAMPLES> UNDER 'OPTIONS', SET THE CONFIDENCE LEVEL 95.0 AND ALTERNATE AS 'LESS THAN'> OK

B.) THE VALUE OF THE TEST STATISTIC IS T= -4.26

C.) THE OBSERVED P-VALUE IS 0.001 AND THE ESTIMATED D.F IS D.F=9

  

D.) AS P-VALUE IS LESS THAN 0.05( LEVEL OF SIGNIFICANCE), WE REJECT THE NULL HYPOTHESIS AND CONCLUDE THAT AVERAGE CRUISE TO CARIBBEAN IS CHEAPER AS COMPARED TO ALASKA.

E.) AT 0.01 LEVEL OF SIGNIFICANCE, WE REPEAT THE ABOVE EXPERIMENT, SETTING THE CONFIDENCE LEVEL AS 99.0

OBSERVATION- T-VALUE=-4.26, D.F=9, P-VALUE=0.001

AS THE P-VALUE IS LESS THAN 0.01(LEVEL OF SIGNIFICANCE), WE REJECT THE NULL HYPOTHESIS AND CONCLUDE THAT AVERAGE CRUISE TO CARIBBEAN IS CHEAPER AS COMPARED TO ALASKA.

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