eBook Exercise 8.3 (Algorithmic A simple random sample of 20 items resulted in a
ID: 3207724 • Letter: E
Question
eBook Exercise 8.3 (Algorithmic A simple random sample of 20 items resulted in a sample mean of 10. The population standard deviation is 10 a. Compute the 95% confidence interval for the population mean. Round your answers to one decimal place. Enter your answer using parentheses and a comma in the form (n1,n2) Do not use mas in your numerical answer (i.e. use 1200 instead of 1,200 etc.) b. Assume that the same sample mean was obtained from a sample of 120 items. Provide a 95% confidence interval for the population mean. Round your answers to two decimal places c. What is the effect of a larger sample size on the interval estimate? Larger sample provides a Select your answer margin of error.Explanation / Answer
a.
Confidence Interval
CI = x ± Z a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=10
Standard deviation( sd )=10
Sample Size(n)=20
Confidence Interval = [ 10 ± Z a/2 ( 10/ Sqrt ( 20) ) ]
= [ 10 - 1.96 * (2.24) , 10 + 1.96 * (2.24) ]
= [ 5.62,14.38 ] ~ [ 5.6, 14.4 ]
b.
Sample Size(n)=120
Confidence Interval = [ 10 ± Z a/2 ( 10/ Sqrt ( 120) ) ]
= [ 10 - 1.96 * (0.9) , 10 + 1.96 * (0.9) ]
= [ 8.2,11.8 ]
c.
Larger sample provides a decreased margin of error
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