We can find the roots of a quadratic function by looking at where it intercepts the x-axis. If a graph is entirely above the x-a
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Step-by-step explanation:
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Answer:
A 90% confidence interval for the standard deviation of the fracture toughness distribution is [4.06, 6.82].
Step-by-step explanation:
We are given the following observations that were made on fracture toughness of a base plate of 18% nickel maraging steel below;
68.6, 71.9, 72.6, 73.1, 73.3, 73.5, 75.5, 75.7, 75.8, 76.1, 76.2, 76.2, 77.0, 77.9, 78.1, 79.6, 79.8, 79.9, 80.1, 82.2, 83.7, 93.4.
Firstly, the pivotal quantity for finding the confidence interval for the standard deviation is given by;
P.Q. = ~
where, s = sample standard deviation = = 5.063
= population standard deviation
n = sample of observations = 22
Here for constructing a 90% confidence interval we have used One-sample chi-square test statistics.
<u>So, 90% confidence interval for the population standard deviation, </u><u> is ;</u>
P(11.59 < < 32.67) = 0.90 {As the critical value of chi at 21 degrees
of freedom are 11.59 & 32.67}
P(11.59 < < 32.67) = 0.90
P( <
<
) = 0.90
P( <
<
) = 0.90
<u>90% confidence interval for</u> = [
,
]
= [ ,
]
= [16.48 , 46.45]
<u>90% confidence interval for</u> = [
,
]
= [4.06 , 6.82]
Therefore, a 90% confidence interval for the standard deviation of the fracture toughness distribution is [4.06, 6.82].