Confidence Intervals Stu uppose you per semester. You collect 45 observations. d

Question

Confidence Intervals Stu uppose you per semester. You collect 45 observations. deviation of 2.6 population mean number of classes an SVSU student takes ions, with a sample mean of 3.42 and a sample standard want to estimate the mean point estimate for the population mean? 22. What is is a 95% confidence interval estimate for the population mean? 23, write down an interpretation of your 95% confidence interval. 24. what is a 99% confidence interval estimate for the population mean? 25, suppose that you have 100 observations instead of 45, what is a 95% confidence interval estimate for the population mean?

Explanation / Answer

Ans a)

Point Estimate for the population mean is Sampe Mean hene inour case point estimate of sample mean wil be 3.42

Ans b)

95% confiedance interval for population mean

for 95% confiedance interval z value is 1.96 then interval will be calculated by

(Sample mean-z*Sample standard deviation,Sample mean+z*Sample standard deviation)

(3.42-1.96*2.6/sqrt(45),3.42+1.96*2.6/sqrt(45))=(2.660,4.179)

Ans C)

We are 95% sure that according to this sample population mean resides in between 2.660 and 4.179

Ans D)

z(alpha/2)=z(0.495)=2.576

(3.42-2.576*2.6/sqrt(45),3.42+2.576*2.6/sqrt(45))=(2.421,4.412)

Ans E)

Now sample size is 100 then for 95% confiedance interval will be

( (3.42-1.96*2.6/sqrt(100),3.42+1.96*2.6/sqrt(100))=(2.75,4.089)

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