Researchers argue SAT scores should not be used as a measure of math ability of seniors...

Researchers argue SAT scores should not be used as a measure of math ability of seniors in California, since only a minority of students take the test. They argue if all seniors took the test the score would not be not more than 450. The α of the math SAT is 100. The researchers gave you random sample of 500 seniors from California the test. The mean of their mouths were x̅ =461. Is this good evidence against the claim that the mean of California seniors is no more than 450, at α = 0.01 ? Use the P -value approach

Solutions

Expert Solution

SOLUTION-

WE WANT TO TEST THE CLAIM THAT MEAN OF CALIFORNIA SENIORS IS NO MORE THAN 450. SO THE HYPOTHESIS FRAMED IS,

SUMMARISED DATA:

SAMPLE SIZE(n) = 500

SAMPLE MEAN= 461

POPULATION SD = 100

LEVEL OF SIGNIFICANCE = 0.01

WE PERFORM A ONE SAMPLE-Z TEST AS THE POPULATION SD IS GIVEN. WE USE MINITAB-16 FOR THE COMPUTATION PURPOSE.

STEPS- STAT> BASIC STATISTICS> ONE SAMPLE-Z> ENTER THE SAMPLE MEAN AND SAMPLE SIZE> ENTER THE STANDARD DEVIATION> ENTER THE HYPOTHESIZED MEAN AS 450> UNDER 'OPTIONS', ENTER THE CONFIDENCE LEVEL AS 99.0 AND ALTERNATE AS 'GREATER THAN'> OK

OBSERVATIONS-

THE TEST STATISTIC Z=2.46 AND THE CORRESPONDING P-VALUE IS 0.007

AS THE P-VALUE< LEVEL OF SIGNIFICANCE, WE REJECT THE NULL HYPOTHESIS AND CONCLUDE THAT THE MEAN OF CALIFORNIA SENIORS IS NO MORE THAN 450.

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

orchestra answered 2 years ago

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