Respuesta :
Answer:
The confidence interval is [240.87 , 247.13].
Step-by-step explanation:
Given : The standard deviation of the weights of elephants is known to be approximately 15 pounds. We wish to construct a 95% confidence interval for the mean weight of newborn elephant calves. Fifty newborn elephants are weighed. The sample mean is 244 pounds. The sample standard deviation is 11 pounds.
To find : Construct a 95% confidence interval for the population mean weight of newborn elephants. State the confidence interval?
Solution :
We have given that,
Sample mean, x =244
Standard deviation, s =11
Sample size, n =50
First we find the standard error,
[tex]\text{Standard error}=\frac{s}{\sqrt n}[/tex]
[tex]\text{Standard error}=\frac{11}{\sqrt{50}}[/tex]
[tex]\text{Standard error}=1.56[/tex]
Then we find the margin of error,
[tex]\text{Margin of error}=t_{\frac{\alpha}{2}}\times\text{Standard error} [/tex]
Applying t-table values,
[tex]t_{\frac{\alpha}{2}}[/tex] is the t-table value
Level of significance, [tex]\alpha = 0.05[/tex]
From standard normal table, two tailed value of with n-1 = 49 d.f is [tex]t_{\frac{\alpha}{2}}=2.01[/tex]
Substitute in the formula,
[tex]\text{Margin of error}=2.01\times1.56[/tex]
[tex]\text{Margin of error}=3.1356[/tex]
Now, The confidence of the interval is given by,
[tex]CI = x\pm \text{Margin of error}[/tex]
[tex]CI = 244\pm3.1356[/tex]
[tex]CI = 244-3.1356,244+3.1356[/tex]
[tex]CI = 240.8644,247.1356[/tex]
Therefore, The confidence interval is[ 240.87 , 247.13 ].
