The following observations were randomly sampled from a Normal distribution. Using this data, construct a 99% confidence interval for the mean and interpret the interval. 8.11 12.06 10.01 12.01 8.59 9.35 10.79 11.74 7.42 11.72 8.44 7.67 10.93 8.42 8.50
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Expert's answer
2021-06-11T02:37:33-0400
xˉ=ni=1∑nxi=15i=1∑15xi
=151(8.11+12.06+10.01+12.01+8.59
+9.35+10.79+11.74+7.42+11.72
+8.44+7.67+10.93+8.42+8.50=15145.76
≈9.717333
s2=15−1i=1∑15(xi−xˉ)2≈2.843450
s=s2≈1.686253
The critical value for α=0.01 and df=n−1=15−1=14 degrees of freedom is tc=2.976842.
The corresponding confidence interval is computed as shown below:
CI=(xˉ−tc×ns,xˉ−tc×ns)
=(9.717333−2.976842×151.686253,
9.717333+2.976842×151.686253)
≈(8.421,11.013)
Therefore, based on the data provided, the 99% confidence interval for the population mean is 8.421<μ<11.013, which indicates that we are 99% confident that the true population mean μ is contained by the interval (8.421,11.013).
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