Respuesta :
Answer:
The 99% confidence interval estimate of the mean head circumference of all 2-month-old babies is (40.18cm, 41.02cm).
Step-by-step explanation:
Our sample size is 100.
The first step to solve this problem is finding our degrees of freedom, that is, the sample size subtracted by 1. So
[tex]df = 100-1 = 99[/tex].
Then, we need to subtract one by the confidence level [tex]\alpha[/tex] and divide by 2. So:
[tex]\frac{1-\alpha}{2} = \frac{0.01}{2} = 0.005[/tex]
Now, we need our answers from both steps above to find a value T in the t-distribution table. So, with 99 and 0.005 in the t-distribution table, we have [tex]T = 2.626[/tex]
Now, we find the standard deviation of the sample. This is the division of the standard deviation by the square root of the sample size. So
[tex]s = \frac{1.6}{\sqrt{100}} = 0.16[/tex]
Now, we multiply T and s
[tex]M = Ts = 2.626*0.16 = 0.42[/tex]
For the lower end of the interval, we subtract the sample mean by M. So the lower end of the interval here is
[tex]L = 40.6 - 0.42 = 40.18[/tex]cm
For the upper end of the interval, we add the sample mean and M. So the upper end of the interval here is
[tex]L = 40.6 + 0.42 = 41.02[/tex]cm
So
The 99% confidence interval estimate of the mean head circumference of all 2-month-old babies is (40.18cm, 41.02cm).
