All Questions
9
questions
1
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0
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26
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Probability that both the mean and sample variance are both covered by their respective confidence intervals?
I am given the question: "What is the probability that both the mean is in its confidence interval for confidence level a and the variance is in its confidence interval for confidence level a?&...
- 11
1
vote
2
answers
2k
views
Standard error of estimated sum or product mean
Updated question: Given two sample means ($\bar X, \bar Y$) and sample standard deviations ($S_X, S_Y$) with different sample sizes ($n_X, n_Y$), I want to calculate the standard errors ($SE_\theta, ...
0
votes
1
answer
348
views
Confidence intervals for averages of averages
Suppose we have an experiment involving $N$ independent samples of single variable functions, $y_1(t),...,y_N(t)$ where $$y_k(t) = \dfrac{1}{M}\sum_{j = 1}^{M} x_j(t); \ \ k = 1,...,N.$$ I am ...
- 53
2
votes
2
answers
132
views
Computing the confidence interval for two samples but getting slightly different answers
Consider two samples $X_1,..,X_k$ and $Y_1,..,Y_m$ where $X_i \sim \mathcal{N}(\mu_x,\,\sigma^{2})\,$ and $Y_i \sim \mathcal{N}(\mu_y,\,\sigma^{2})\,.$ Say $k=m=100$ and $k+m=n$. Say that the ...
- 43
1
vote
1
answer
962
views
Confidence interval for $\sigma^2$
I started with any distribution and underwent the CLT on $\sqrt{n}(\widehat{\sigma}^2 - \sigma^2)$ where
$$
\widehat{\sigma}^2 = \frac{1}{n}\sum_{i=1}^n (X_i - \mu)^2
$$
is a sample mean of $\sigma^2$...
1
vote
1
answer
63
views
Confusion about confidence interval
So far I understand, confidence interval (for mean) is defined by treating the sample mean as a proxy for population mean and then finding a interval where the true mean will be in certain percentage ...
- 535
0
votes
1
answer
93
views
Evaluating A/B test using confidence intervals
I have a situation where I worked on two different flavors of a website say A and B (using some fictitious numbers for illustration). For A the amount of time spent by users went up by 1% for 1 ...
- 119
1
vote
0
answers
175
views
Distribution of the sample mean of a binomial distribution with prior information
Let's say that there is a finite population of $N$ elements which are either $A$ or $B$ (equivalently this could be a binomial random variable with $N$ repetitions and unknown $P(A)=\theta$).
If I ...
- 1,583
2
votes
2
answers
3k
views
How to assess accuracy of phone GPS in measuring distances?
I am a complete stranger to statistics (apart from mandatory courses in college), but lately I ran into an interesting real-world scenario.
Recently I started jogging. I take my GPS phone with me to ...
- 123