Opinion Polls (Cambridge Stats Notes) - Clarification Required
$begingroup$
Looking at these again.
Page 18 describes opinion polls. I understand everything up to where they say this:
$$mathbb{P} left( hat{p} - 0.03 leq p leq hat{p} + 0.03 right) = mathbb{P} left( -frac{0.03}{sqrt{p(1-p)/n}} leq frac{hat{p}-p}{sqrt{p(1-p)/n}} leq frac{0.03}{sqrt{p(1-p)/n}} right)$$
I don't understand how they jump from the lhs to the rhs. Any tips, please?
Also how do they then go to the next line? (the approximate one). Thank you.
EDIT:
I was about to write that I get the following, to obtain $p$ in the middle:
$$mathbb{P} left( hat{p} - eta sqrt{p(p-1)/n} leq p leq hat{p} - xi sqrt{p(1-p)n} right)$$
is this actually useful, hmm
statistics
asked Dec 20 '18 at 17:32
i squared - Keep it Reali squared - Keep it Real
1,62511027
$endgroup$
|
show 4 more comments
$begingroup$
Looking at these again.
Page 18 describes opinion polls. I understand everything up to where they say this:
$$mathbb{P} left( hat{p} - 0.03 leq p leq hat{p} + 0.03 right) = mathbb{P} left( -frac{0.03}{sqrt{p(1-p)/n}} leq frac{hat{p}-p}{sqrt{p(1-p)/n}} leq frac{0.03}{sqrt{p(1-p)/n}} right)$$
I don't understand how they jump from the lhs to the rhs. Any tips, please?
Also how do they then go to the next line? (the approximate one). Thank you.
EDIT:
I was about to write that I get the following, to obtain $p$ in the middle:
$$mathbb{P} left( hat{p} - eta sqrt{p(p-1)/n} leq p leq hat{p} - xi sqrt{p(1-p)n} right)$$
is this actually useful, hmm
statistics
asked Dec 20 '18 at 17:32
i squared - Keep it Reali squared - Keep it Real
1,62511027
$endgroup$
3
$begingroup$
Subtract $hat{p}$ from both sides and divide by $sqrt{p(1-p)/n}$.
$endgroup$
– APC89
Dec 20 '18 at 17:43
$begingroup$
ahhhhhhhhh. I see thanks...
$endgroup$
– i squared - Keep it Real
Dec 20 '18 at 17:47
$begingroup$
very neat. I like it.
$endgroup$
– i squared - Keep it Real
Dec 20 '18 at 17:48
$begingroup$
You are welcome.
$endgroup$
– APC89
Dec 20 '18 at 17:49
$begingroup$
um the numerator is then $p-hat{p}$
$endgroup$
– i squared - Keep it Real
Dec 20 '18 at 17:53
|
show 4 more comments
$begingroup$
Looking at these again.
Page 18 describes opinion polls. I understand everything up to where they say this:
$$mathbb{P} left( hat{p} - 0.03 leq p leq hat{p} + 0.03 right) = mathbb{P} left( -frac{0.03}{sqrt{p(1-p)/n}} leq frac{hat{p}-p}{sqrt{p(1-p)/n}} leq frac{0.03}{sqrt{p(1-p)/n}} right)$$
I don't understand how they jump from the lhs to the rhs. Any tips, please?
Also how do they then go to the next line? (the approximate one). Thank you.
EDIT:
I was about to write that I get the following, to obtain $p$ in the middle:
$$mathbb{P} left( hat{p} - eta sqrt{p(p-1)/n} leq p leq hat{p} - xi sqrt{p(1-p)n} right)$$
is this actually useful, hmm
statistics
asked Dec 20 '18 at 17:32
i squared - Keep it Reali squared - Keep it Real
1,62511027
$endgroup$
Looking at these again.
Page 18 describes opinion polls. I understand everything up to where they say this:
$$mathbb{P} left( hat{p} - 0.03 leq p leq hat{p} + 0.03 right) = mathbb{P} left( -frac{0.03}{sqrt{p(1-p)/n}} leq frac{hat{p}-p}{sqrt{p(1-p)/n}} leq frac{0.03}{sqrt{p(1-p)/n}} right)$$
I don't understand how they jump from the lhs to the rhs. Any tips, please?
Also how do they then go to the next line? (the approximate one). Thank you.
EDIT:
I was about to write that I get the following, to obtain $p$ in the middle:
$$mathbb{P} left( hat{p} - eta sqrt{p(p-1)/n} leq p leq hat{p} - xi sqrt{p(1-p)n} right)$$
is this actually useful, hmm
statistics
statistics
asked Dec 20 '18 at 17:32
i squared - Keep it Reali squared - Keep it Real
1,62511027
asked Dec 20 '18 at 17:32
i squared - Keep it Reali squared - Keep it Real
1,62511027
edited Dec 20 '18 at 17:47
i squared - Keep it Real
asked Dec 20 '18 at 17:32
i squared - Keep it Reali squared - Keep it Real
1,62511027
asked Dec 20 '18 at 17:32
i squared - Keep it Reali squared - Keep it Real
1,62511027
asked Dec 20 '18 at 17:32
i squared - Keep it Reali squared - Keep it Real
1,62511027
1,62511027
3
$begingroup$
Subtract $hat{p}$ from both sides and divide by $sqrt{p(1-p)/n}$.
$endgroup$
– APC89
Dec 20 '18 at 17:43
$begingroup$
ahhhhhhhhh. I see thanks...
$endgroup$
– i squared - Keep it Real
Dec 20 '18 at 17:47
$begingroup$
very neat. I like it.
$endgroup$
– i squared - Keep it Real
Dec 20 '18 at 17:48
$begingroup$
You are welcome.
$endgroup$
– APC89
Dec 20 '18 at 17:49
$begingroup$
um the numerator is then $p-hat{p}$
$endgroup$
– i squared - Keep it Real
Dec 20 '18 at 17:53
|
show 4 more comments
3
$begingroup$
Subtract $hat{p}$ from both sides and divide by $sqrt{p(1-p)/n}$.
$endgroup$
– APC89
Dec 20 '18 at 17:43
$begingroup$
ahhhhhhhhh. I see thanks...
$endgroup$
– i squared - Keep it Real
Dec 20 '18 at 17:47
$begingroup$
very neat. I like it.
$endgroup$
– i squared - Keep it Real
Dec 20 '18 at 17:48
$begingroup$
You are welcome.
$endgroup$
– APC89
Dec 20 '18 at 17:49
$begingroup$
um the numerator is then $p-hat{p}$
$endgroup$
– i squared - Keep it Real
Dec 20 '18 at 17:53
3
3
$begingroup$
Subtract $hat{p}$ from both sides and divide by $sqrt{p(1-p)/n}$.
$endgroup$
– APC89
Dec 20 '18 at 17:43
$begingroup$
Subtract $hat{p}$ from both sides and divide by $sqrt{p(1-p)/n}$.
$endgroup$
– APC89
Dec 20 '18 at 17:43
$begingroup$
ahhhhhhhhh. I see thanks...
$endgroup$
– i squared - Keep it Real
Dec 20 '18 at 17:47
$begingroup$
ahhhhhhhhh. I see thanks...
$endgroup$
– i squared - Keep it Real
Dec 20 '18 at 17:47
$begingroup$
very neat. I like it.
$endgroup$
– i squared - Keep it Real
Dec 20 '18 at 17:48
$begingroup$
very neat. I like it.
$endgroup$
– i squared - Keep it Real
Dec 20 '18 at 17:48
$begingroup$
You are welcome.
$endgroup$
– APC89
Dec 20 '18 at 17:49
$begingroup$
You are welcome.
$endgroup$
– APC89
Dec 20 '18 at 17:49
$begingroup$
um the numerator is then $p-hat{p}$
$endgroup$
– i squared - Keep it Real
Dec 20 '18 at 17:53
$begingroup$
um the numerator is then $p-hat{p}$
$endgroup$
– i squared - Keep it Real
Dec 20 '18 at 17:53
|
show 4 more comments
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3
$begingroup$
Subtract $hat{p}$ from both sides and divide by $sqrt{p(1-p)/n}$.
$endgroup$
– APC89
Dec 20 '18 at 17:43
$begingroup$
ahhhhhhhhh. I see thanks...
$endgroup$
– i squared - Keep it Real
Dec 20 '18 at 17:47
$begingroup$
very neat. I like it.
$endgroup$
– i squared - Keep it Real
Dec 20 '18 at 17:48
$begingroup$
You are welcome.
$endgroup$
– APC89
Dec 20 '18 at 17:49
$begingroup$
um the numerator is then $p-hat{p}$
$endgroup$
– i squared - Keep it Real
Dec 20 '18 at 17:53