Question

1. A SRS of 30 commuters to the Los Angeles metropolitan area are selected, and each is asked how far they commute to work each day. In the sample, the mean distance is 64 miles and the standard deviation is 12 miles. Is there evidence that the average commute to work for this population is more than 60 miles?

a. Yes, since the p-value is less than 0.05.

b. No, since the p-value is less than 0.05.

c. No, since the p-value is greater than 0.05.

d. Yes, since the p-value is greater than 0.05.

Answer 1

SOLUTION-

WE USE MINITAB-16 TO CARRY OUT THE CALCULATIONS

WE PERFORM A ONE-SAMPLE T TEST AS THE SAMPLE STANDARD DEVIATION IS KNOWN.

SAMPLE SIZE(n)= 30, SAMPLE MEAN()= 64, SAMPLE STANDARD DEVIATION()= 12

ALSO, THE HYPOTHESIZED MEAN()= 60

THE HYPOTHESIS FRAMED IS,

STEPS- STAT> BASIC STATISTICS> ONE-SAMPLE T> ENTER THE SUMMARIZED DATA> UNDER 'OPTIONS', SET THE CONFIDENCE LEVEL AS 0.05; ALSO THE ALTERNATIVE IS 'GREATER THAN'> OK

OBSERVATIONS- VALUE OF TEST STATISTIC IS 1.83 AND P-VALUE IS 0.039

CONCLUSION- AS THE P-VALUE IS LESS THAN 0.05(LEVEL OF CONFIDENCE), WE REJECT THE NULL HYPOTHESIS AND CONCLUDE THAT AVERAGE COMMUTE TO WORK FOR POPULATION IS MORE THAN 60 MILES.

ANSWER-(A) YES, THERE IS EVIDENCE, SINCE THE P-VALUE IS LESS THAN 0.05

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