Respuesta :
Answer:
The 95% of confidence interval for the mean penetration resistance for this soil is (2.0823, 3.1977).
Step-by-step explanation:
The sample size is 15.
The first step to solve this problem is finding how many degrees of freedom there are, that is, the sample size subtracted by 1. So
[tex]df = 15-1 = 14[/tex]
Then, we need to subtract one by the confidence level [tex]\alpha[/tex] and divide by 2. So:
[tex]\frac{1-0.95}{2} = \frac{0.05}{2} = 0.025[/tex]
Now, we need our answers from both steps above to find a value T in the t-distribution table. So, with 14 and 0.025 in the t-distribution table, we have [tex]T = 2.145[/tex].
Now, we need to find the standard deviation of the sample. That is:
[tex]s = \frac{1.02}{\sqrt{15}} = 0.26[/tex]
Now, we multiply T and s
[tex]M = T*s = 2.145*0.26 = 0.5577[/tex]
For the lower end of the interval, we subtract the mean by M. So 2.64 - 0.5577 = 2.0823
For the upper end of the interval, we add the mean to M. So 2.64 + 0.5577 = 3.1977
The 95% of confidence interval for the mean penetration resistance for this soil is (2.0823, 3.1977).
