Question 1063468: (5 points) For the following data set
136 141 137 145
131 135 138 136
130 132 136 134
137 133 141 139
Table 2: Data set Exercise 2
Construct a
1. 90% confidence interval for the population mean;
2. 95% confidence interval for the population mean;
3. 99% confidence interval for the population mean;
4. What assumption do you need to make about the population of interest to construct the confidence
intervals
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! The mean of x is 136.31 to two decimal places
s=3.96
The general form of a CI is
for ci of 1-alpha, x bar+/- t(df=15,alpha/2)s/sqrt (n)
so for 90%, where t=1.753, 136.31+/-1.753*(3.96/4)=136.31 +/-1.74 or (134.57, 138.05)
for 95%, where t=2.1314, 136.31+/- 2.1314*0.99=136.31+/-2.11 or (134.20, 138.42)
for 99%, where t=2.9467, 136.31+/- 2.9467*0.99=136.31+/-2.92 or (133.39, 139.23)
Assumptions: population is normally distributed and standard deviation of the sample is an unbiased estimator of the standard deviation of the population.
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