blazerqb11
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- Joined
- Apr 17, 2016
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In my probability class we were given the following problem:
Suppose you take a sample of your friends and measure their heights. You calculate the sample mean to be 5 feet tall and the sample standard deviation to be 1 foot.
a. If the number of people you sampled was five, what is the lowest value of ? for which we will get the sample mean you calculated at least 95% of the time?
b. If the number of people you sampled was 1000, what is the lowest value of ? for which we will get the sample mean you calculated at least 95% of the time?
c. If the number of people you sampled was infinite, what is the lowest value of for which we will get the sample mean you calculated at least 95% of the time?
And we were pointed to Theorem 8.4 on the this page to help us. However, I'm having a hard time seeing how that applies directly. Down below that it talks about confidence intervals, which use the t-disto, which seems to be more applicable. Are those just part of the same theorem?
I used \(\displaystyle \left[\overline{X}- t_{\frac{\alpha}{2},n-1}\frac{S}{\sqrt{n}} , \overline{X}+ t_{\frac{\alpha}{2},n-1} \frac{S}{\sqrt{n}}\right] \) to solve the problems and got the following answers, but I am not sure at all that they are correct
a. (3.76,6.24) is the interval so 3.764 should be the answer
b. (4.94,5.06) so 4.94
c. (5,5) so 5
Suppose you take a sample of your friends and measure their heights. You calculate the sample mean to be 5 feet tall and the sample standard deviation to be 1 foot.
a. If the number of people you sampled was five, what is the lowest value of ? for which we will get the sample mean you calculated at least 95% of the time?
b. If the number of people you sampled was 1000, what is the lowest value of ? for which we will get the sample mean you calculated at least 95% of the time?
c. If the number of people you sampled was infinite, what is the lowest value of for which we will get the sample mean you calculated at least 95% of the time?
And we were pointed to Theorem 8.4 on the this page to help us. However, I'm having a hard time seeing how that applies directly. Down below that it talks about confidence intervals, which use the t-disto, which seems to be more applicable. Are those just part of the same theorem?
I used \(\displaystyle \left[\overline{X}- t_{\frac{\alpha}{2},n-1}\frac{S}{\sqrt{n}} , \overline{X}+ t_{\frac{\alpha}{2},n-1} \frac{S}{\sqrt{n}}\right] \) to solve the problems and got the following answers, but I am not sure at all that they are correct
a. (3.76,6.24) is the interval so 3.764 should be the answer
b. (4.94,5.06) so 4.94
c. (5,5) so 5