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Question :

A manufacturer of car batteries claims that his batteries will last, on average, 3 years with a variance of 1 year. If 5 of this batteries have lifetimes of 1.9, 2.4, 3.0, 3.5 and 4.2 years, construct a 95% confidence interval for $\sigma^2$ and decide if the manufacturer's claim that $\sigma^2= 1 $ is valid. Assume the population of battery lives to be approximately normally distributed.

Answer : $0.293 < \sigma^2 < 6.736$. Since this interval contains the value 1, the claim that $\sigma^2 = 1$ is valid.

I tried this : the result seems quite different from the given answer. enter image description here

Where did I do wrong?

Moreover, I do not understand well the answer "Since this interval contains the value 1, the claim that $\sigma^2 = 1$ is valid.". Can you explain more?

hola
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Casper
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  • Suggestion to use math mode for formatting, and not screenshot of handwritten note. – hola Dec 29 '18 at 08:54

1 Answers1

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for $(n-1)s^2$ you just calculate the sum of squared errors (SSE).

$s^2=\frac{1}{n-1}\cdot SSE \Rightarrow (n-1) \cdot s^2= SSE$

greetings,

calculus

callculus42
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