Question

Previous 21 22 23 24 25 26 Next Question 21 of 26 (3 points) 7.3 Section Exercise 11 A sample of 9 adult elephants had an average weight of 11,965 pounds. The standard deviation for the sample was 24 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.

Answer 1

21 ) Given : Sample size = n=9

Sample mean=$\bar{X}$=11965

Sample standard deviation=s=24

Significance level=$\alpha$=0.10

Therefore , the 90% confidence interval of the population mean for the weights of adult elephants is ,

$\bar{X}\pm t_{\alpha/2,n-1}\frac{s}{\sqrt{n}}$

$11965\pm t_{0.10/2,9-1}\frac{24}{\sqrt{9}}$

$11965\pm 1.860*8$ ; From t-table $t_{0.10/2,9-1}=1.860$

$11965\pm 14.880$

$11950.12\approx 11950<\mu<11979.88\approx 11980$

22)

21 ) Given : Sample size = n=10

Sample mean=$\bar{X}$=14

Sample standard deviation=s=4.4

Significance level=$\alpha$=0.01

Therefore , the 99% confidence interval of the mean is ,

$\bar{X}\pm t_{\alpha/2,n-1}\frac{s}{\sqrt{n}}$

$14\pm t_{0.01/2,10-1}\frac{4.4}{\sqrt{10}}$

$14\pm 3.250*1.3914$ ; from excel ,$t_{0.01/2,10-1}=3.250$

$14\pm 4.5221$

$9.48<\mu<18.52$