Answer :
Answer:
The correct option is (C) (2.769, 3.231).
Step-by-step explanation:
The confidence interval for mean when the standard deviation is not known is:
[tex]CI=\bar x\pm t_{\alpha/2, (n-1)}\frac{s}{\sqrt{n}}[/tex]
Given:
[tex]\bar x = 3\\s=0.3\\n=9\\\alpha =1-0.95=0.05[/tex]
Compute the critical value as follows:
[tex]t_{\alpha/2, (n-1)}=t_{0.05/2, (9-1)}=t_{0.025, 8}=2.31[/tex]
**Use a t-table.
The 95% confidence interval for true mean length of the bolt is:
[tex]CI=\bar x\pm t_{\alpha/2, (n-1)}\frac{s}{\sqrt{n}}\\=3\pm 2.31\times \frac{0.30}{\sqrt{9}}\\ =3\pm 0.231\\=(2.769, 3.231)[/tex]
Thus, the 95% confidence interval for true mean length of the bolt is (2.769, 3.231).
The correct option is (C).