Here are summary statistics fro randomly selected weights of

kuhse4461a 2021-12-13 Answered
Here are summary statistics fro randomly selected weights of newborn girs:
n=240, x=26.1hg, s=6.3hg
Construct a confidence interval estimate of the mean. Use a 99% confidence level. Are these results very different from the confidence interval
25.1hg<μ<28.1hg
with only 13 sample values,
x=26.6hg and s=1.8hg?
What is the confidence interval for the population mean μ?
Are the results between the two confidence intervals very different?
a) No, because each confidence interval contains the mean of the other confidence interval.
b) No, because the confidence interval limits are similar.
c) Yes, because the confidence interval limits are not similar.
d) Yes, because one confidence interval does not contain the mean of the other confidence interval.
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Expert Answer

movingsupplyw1
Answered 2021-12-14 Author has 30 answers
Step 1
The confidence interval is used to infer about the population parameter. The confidence interval provides the range of plausible values of the population parameter.
If the sample size is sufficiently large, the confidence interval can be estimated by the standard normal distribution and the confidence interval is given by
x±z×(sn)
When the sample size is small the confidence interval is computed using the students
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porschomcl
Answered 2021-12-15 Author has 28 answers

Step 1
Given:
n=240
x=26.1 hg
s=6.3 hg
σ=0.01
Step 2
99%Cl:
(xtn1, α2×sn<μ<x+tn1, α2×sn)
(26.1t239, 0.005×6.3240<μ<26.1+t239, 0.005×6.3240)
(26.12.5965562×6.3240<μ<26.1+2.5965562×6.3240)
(25.0 hg<μ<27.2 hg)
This interval is n  compared to
25.1 hg<μ<28.1 hg
with,
n=13, s=1.8 hg, x=26.6 hg

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New questions

I recently have this question:
I have a bag of toys. 10% of the toys are balls. 10% of the toys are blue.
If I draw one toy at random, what're the odds I'll draw a blue ball?
One person provided an answer immediately and others suggested that more details were required before an answer could even be considered. But, there was a reason I asked this question the way that I did.
I was thinking about probabilities and I was coming up with a way to ask a more complicated question on math.stackexchange.com. I needed a basic example so I came up with the toys problem I posted here.
I wanted to run it by a friend of mine and I started by asking the above question the same way. When I thought of the problem, it seemed very clear to me that the question was "what is P ( b l u e b a l l )." I thought the calculation was generally accepted to be
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When I asked my friend, he said, "it's impossible to know without more information." I was baffled because I thought this is what one would call "a priori probability."
I remember taking statistics tests in high school with questions like "if you roll two dice, what're the odds of rolling a 7," "what is the probability of flipping a coin 3 times and getting three heads," or "if you discard one card from the top of the deck, what is the probability that the next card is an ace?"
Then, I met math.stackexchange.com and found that people tend to talk about "fair dice," "fair coins," and "standard decks." I always thought that was pedantic so I tested my theory with the question above and it appears you really need to specify that "the toys are randomly painted blue."
It's clear now that I don't know how to ask a question about probability.
Why do you need to specify that a coin is fair?
Why would a problem like this be "unsolvable?"
If this isn't an example of a priori probability, can you give one or explain why?
Why doesn't the Principle of Indifference allow you to assume that the toys were randomly painted blue?
Why is it that on math tests, you don't have to specify that the coin is fair or ideal but in real life you do?
Why doesn't anybody at the craps table ask, "are these dice fair?"
If this were a casino game that paid out 100 to 1, would you play?
This comment has continued being relevant so I'll put it in the post:
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