Respuesta :
Answer:
95% two-sided confidence interval on the true mean breaking strength is (94.8cm, 99.2cm)
Step-by-step explanation:
Our sample size is 11.
The first step to solve this problem is finding our degrees of freedom, that is, the sample size subtracted by 1. So
[tex]df = 11-1 = 10[/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 10 and 0.025 in the two-sided t-distribution table, we have [tex]T = 1.812[/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{4}{\sqrt{11}} = 1.2060[/tex]
Now, we multiply T and s
[tex]M = Ts = 1.812*1.2060 = 2.19/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 = 97 - 2.19 = 94.81 = 94.8[/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 = 97 + 2.19 = 99.19 = 99.2[/tex]cm
So
95% two-sided confidence interval on the true mean breaking strength is (94.8cm, 99.2cm).
