Question

weights of elephants a sample of 8 adult elephants had an average weight of 11,995 pounds. the standard deviation for the sample was 27 pounds. find the 90% confidence interval of the population mean for the weights of adult elephants. assume the variable is normally distributed. round intermediate answers to at least three decimal places. round your final answers to the nearest whole number.
$\square < \mu < \square$

Explanation:

Step1: Identify key values

Sample size $n=8$, sample mean $\bar{x}=11995$, sample standard deviation $s=27$, confidence level 90%.

Step2: Find t-critical value

Degrees of freedom $df=n-1=7$. For 90% confidence, $t_{0.05,7}=1.895$.

Step3: Calculate standard error

Standard error $SE=\frac{s}{\sqrt{n}}=\frac{27}{\sqrt{8}}\approx9.5459$.

Step4: Compute margin of error

Margin of error $E=t_{critical}\times SE=1.895\times9.5459\approx18.09$.

Step5: Find confidence interval

Lower bound: $\bar{x}-E=11995-18.09\approx11977$; Upper bound: $\bar{x}+E=11995+18.09\approx12013$.

Answer:

11977 < μ < 12013