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    Recall that the SAT math test has a theoretical mean of 500 and a standard deviation of 100:
    Suppose a sample of 50 mathematically -gifted youngsters scored a mean of 560 on the SAT math test.
    What would the 90 percent confidence limits be?
    What would the 99 percent confidence limits be for the same sample?

    © BrainMass Inc. brainmass.com December 24, 2021, 4:56 pm ad1c9bdddf
    https://brainmass.com/statistics/hypothesis-testing/confidence-limits-theoretical-mean-16993

    SOLUTION This solution is FREE courtesy of BrainMass!

    Recall that the SAT math test has a theoretical mean of 500 and a standard deviation of 100:
    Suppose a sample of 50 mathematically -gifted youngsters scored a mean of 560 on the SAT math test. What would the 90 percent confidence limits be? What would the 99 percent confidence limits be for the same sample?

    What would the 90 percent confidence limits be

    Mean= 500
    Standard deviation = 100
    sample size=n= 50
    standard error of mean= standard deviation. square root of n= 14.1421 = ( 100 /square root of 50)

    Confidence level= 90%
    alpha= 10% =100% -90%
    Or Significance level= 0.10 (expressed as a number )
    No of tails= 2

    Since sample size= 50 >= 30 use normal distribution

    sample mean= 560

    Z at the 0.1 level of significance= 1.6449 (read from the tables or using Excel function NORMSINV)

    Upper confidence limit= mean + z X standard error = 523 =500+1.6449*14.1421
    Lower confidence limit= mean - z X standard error 477 =500-1.6449*14.1421

    Answer:

    Upper confidence limit= 523
    Lower confidence limit= 477

    What would the 99 percent confidence limits be

    Mean= 500
    Standard deviation = 100
    sample size=n= 50
    standard error of meanstandard deviation/ square root of n= 14.1421 = ( 100 /square root of 50)

    Confidence level= 99%
    alpha= 1% =100% -99%
    Or Significance level=alpha= 0.01 (expressed as a number )
    No of tails= 2

    Since sample size= 50 >= 30 use normal distribution

    sample mean= 560

    Z at the 0.01 level of significance= 2.5758 (read from the tables or using Excel function NORMSINV)

    Upper confidence limit= mean + z X standard error= 536 =500+2.5758*14.1421
    Lower confidence limit= mean - z X standard error= 464 =500-2.5758*14.1421

    Answer:

    Upper confidence limit= 536
    Lower confidence limit= 464

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 4:56 pm ad1c9bdddf>
    https://brainmass.com/statistics/hypothesis-testing/confidence-limits-theoretical-mean-16993

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