In a manufacturing process a random sample of 9 bolts manufactured has a mean length of 3 inches with a standard deviation of .3 inches. Wha

Question

In a manufacturing process a random sample of 9 bolts manufactured has a mean length of 3 inches with a standard deviation of .3 inches. What is the 95% confidence interval for the true mean length of the bolt?
A. 2.804 to 3.196
B. 2.308 to 3.692
C. 2.769 to 3.231
D. 2.412 to 3.588
E. 2.814 to 3.186

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Josie 2 weeks 2021-11-10T04:55:48+00:00 1 Answer 0 views 0

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    2021-11-10T04:57:02+00:00

    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:

    CI=\bar x\pm t_{\alpha/2, (n-1)}\frac{s}{\sqrt{n}}

    Given:

    \bar x = 3\\s=0.3\\n=9\\\alpha =1-0.95=0.05

    Compute the critical value as follows:

    t_{\alpha/2, (n-1)}=t_{0.05/2, (9-1)}=t_{0.025, 8}=2.31

    **Use a t-table.

    The 95% confidence interval for true mean length of the bolt is:

    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)

    Thus, the 95% confidence interval for true mean length of the bolt is (2.769, 3.231).

    The correct option is (C).

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