95% Confidence Interval for $sigma^2$ & Determining the Reliability of the Claim
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.
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?
statistics
edited Dec 29 '18 at 9:28
pushpen.paul
1,020721
asked May 2 '14 at 5:21
KinKin
55421330
add a comment |
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.
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?
statistics
edited Dec 29 '18 at 9:28
pushpen.paul
1,020721
asked May 2 '14 at 5:21
KinKin
55421330
Suggestion to use math mode for formatting, and not screenshot of handwritten note.
– pushpen.paul
Dec 29 '18 at 8:54
add a comment |
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.
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?
statistics
edited Dec 29 '18 at 9:28
pushpen.paul
1,020721
asked May 2 '14 at 5:21
KinKin
55421330
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.
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?
statistics
statistics
edited Dec 29 '18 at 9:28
pushpen.paul
1,020721
asked May 2 '14 at 5:21
KinKin
55421330
edited Dec 29 '18 at 9:28
pushpen.paul
1,020721
asked May 2 '14 at 5:21
KinKin
55421330
edited Dec 29 '18 at 9:28
pushpen.paul
1,020721
edited Dec 29 '18 at 9:28
pushpen.paul
1,020721
edited Dec 29 '18 at 9:28
pushpen.paul
1,020721
1,020721
asked May 2 '14 at 5:21
KinKin
55421330
asked May 2 '14 at 5:21
KinKin
55421330
asked May 2 '14 at 5:21
KinKin
55421330
55421330
Suggestion to use math mode for formatting, and not screenshot of handwritten note.
– pushpen.paul
Dec 29 '18 at 8:54
add a comment |
Suggestion to use math mode for formatting, and not screenshot of handwritten note.
– pushpen.paul
Dec 29 '18 at 8:54
Suggestion to use math mode for formatting, and not screenshot of handwritten note.
– pushpen.paul
Dec 29 '18 at 8:54
Suggestion to use math mode for formatting, and not screenshot of handwritten note.
– pushpen.paul
Dec 29 '18 at 8:54
add a comment |
1 Answer
1
active
oldest
votes
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
answered May 2 '14 at 8:08
callculuscallculus
17.9k31427
You don't have to sign your messages.
– man on laptop
Jun 16 '15 at 10:51
@user3491648 Yes, I know. It was in my early times here on MSE.
– callculus
Jun 16 '15 at 10:54
Sorry your post turned up in the Closed Vote queue.
– man on laptop
Jun 16 '15 at 10:56
@user3491648 I see. It seems, that somebody is very active in closing posts.
– callculus
Jun 16 '15 at 11:00
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
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
answered May 2 '14 at 8:08
callculuscallculus
17.9k31427
You don't have to sign your messages.
– man on laptop
Jun 16 '15 at 10:51
@user3491648 Yes, I know. It was in my early times here on MSE.
– callculus
Jun 16 '15 at 10:54
Sorry your post turned up in the Closed Vote queue.
– man on laptop
Jun 16 '15 at 10:56
@user3491648 I see. It seems, that somebody is very active in closing posts.
– callculus
Jun 16 '15 at 11:00
add a comment |
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
answered May 2 '14 at 8:08
callculuscallculus
17.9k31427
You don't have to sign your messages.
– man on laptop
Jun 16 '15 at 10:51
@user3491648 Yes, I know. It was in my early times here on MSE.
– callculus
Jun 16 '15 at 10:54
Sorry your post turned up in the Closed Vote queue.
– man on laptop
Jun 16 '15 at 10:56
@user3491648 I see. It seems, that somebody is very active in closing posts.
– callculus
Jun 16 '15 at 11:00
add a comment |
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
answered May 2 '14 at 8:08
callculuscallculus
17.9k31427
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
answered May 2 '14 at 8:08
callculuscallculus
17.9k31427
answered May 2 '14 at 8:08
callculuscallculus
17.9k31427
answered May 2 '14 at 8:08
callculuscallculus
17.9k31427
answered May 2 '14 at 8:08
callculuscallculus
17.9k31427
17.9k31427
You don't have to sign your messages.
– man on laptop
Jun 16 '15 at 10:51
@user3491648 Yes, I know. It was in my early times here on MSE.
– callculus
Jun 16 '15 at 10:54
Sorry your post turned up in the Closed Vote queue.
– man on laptop
Jun 16 '15 at 10:56
@user3491648 I see. It seems, that somebody is very active in closing posts.
– callculus
Jun 16 '15 at 11:00
add a comment |
You don't have to sign your messages.
– man on laptop
Jun 16 '15 at 10:51
@user3491648 Yes, I know. It was in my early times here on MSE.
– callculus
Jun 16 '15 at 10:54
Sorry your post turned up in the Closed Vote queue.
– man on laptop
Jun 16 '15 at 10:56
@user3491648 I see. It seems, that somebody is very active in closing posts.
– callculus
Jun 16 '15 at 11:00
You don't have to sign your messages.
– man on laptop
Jun 16 '15 at 10:51
You don't have to sign your messages.
– man on laptop
Jun 16 '15 at 10:51
@user3491648 Yes, I know. It was in my early times here on MSE.
– callculus
Jun 16 '15 at 10:54
@user3491648 Yes, I know. It was in my early times here on MSE.
– callculus
Jun 16 '15 at 10:54
Sorry your post turned up in the Closed Vote queue.
– man on laptop
Jun 16 '15 at 10:56
Sorry your post turned up in the Closed Vote queue.
– man on laptop
Jun 16 '15 at 10:56
@user3491648 I see. It seems, that somebody is very active in closing posts.
– callculus
Jun 16 '15 at 11:00
@user3491648 I see. It seems, that somebody is very active in closing posts.
– callculus
Jun 16 '15 at 11:00
add a comment |
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Suggestion to use math mode for formatting, and not screenshot of handwritten note.
– pushpen.paul
Dec 29 '18 at 8:54