Assume that IQ scores of college graduates are normally distributed. A researche

Question

Assume that IQ scores of college graduates are normally distributed. A researcher collects a random sample of 24 college graduates and tests their IQ. The sample had a mean IQ of 107.9 with a standard deviation of 15.2. Find a 95% confidence interval for the true mean IQ for college graduates. Provide the right endpoint of the interval as your answer. Round your answer to 1 decimal place. Assume that IQ scores of college graduates are normally distributed. A researcher collects a random sample of 22 college graduates and tests their IQ. The sample had a mean IQ of 107.8 with a standard deviation of 15.5. Find a 95% confidence interval for the true mean IQ for college graduates. Provide the margin of error of the interval as your answer. Round your answer to 1 decimal place.

Explanation / Answer

Q4.
a.
Confidence Interval
CI = x ± t a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
Mean(x)=107.8
Standard deviation( sd )=15.5
Sample Size(n)=22
Confidence Interval = [ 107.8 ± t a/2 ( 15.5/ Sqrt ( 22) ) ]
= [ 107.8 - 2.08 * (3.305) , 107.8 + 2.08 * (3.305) ]
= [ 100.926,114.674 ]
b.
Margin of Error = t a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
ta/2 = t-table value
Mean(x)=107.8
Standard deviation( sd )=15.5
Sample Size(n)=22
Margin of Error = t a/2 * 15.5/ Sqrt ( 22)
= 2.08 * (3.305)
= 6.874

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