Confidence Limits

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

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