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### Choice of null and alternative hypothesis

A firm producing tobacco cigarettes claims that it has discovered a new technique for curing tobacco leaves, that results in an average nicotine content of a cigarette of less than 1.5 mg. To test ...
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### How to interpret MCAR (missing completely at random) any papers that I can read?

When dealing with missing data and Little's missing completely at random test, it's widely considered that if the test has a significance level of P>0.05 the data can be considered as MCAR. But, I ...
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### What fraction to use in the formulation of a hypothesis test ? - Population fraction versus sample fraction

Imagine that I am studying racial discrimination. In particular, whether a white candidate (for a job) is chosen more often than an equally qualified minority candidate. I ask people to choose ...
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### ANOVA for Regression

When using ANOVA to compare means, I understand the null hypothesis is u1=u2=u3.... as we need to combine all groups into a single group when assuming their means are the same. But for ANOVA for ...
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### Definition of alternative hypothesis

Which of these properties is required of the alternative hypothesis, by definition, in the general case: a) If the alternative hypothesis is true, then the null hypothesis would necessarily tend ...
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### Goodness-of-fit test in Logistic regression; which 'fit' do we want to test?

I am referring to the question and its answers: How to compare (probability) predictive ability of models developed from logistic regression? by @Clark Chong and answers/comments by @Frank Harrell. ...
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### What are the ''desirable'' statistical properties of the likelihood ratio test?

I am reading an article whose method is fully based on the likelihood ratio test. The author says that the LR test against one sided alternatives is UMP. He proceeds by claiming that "...even when ...
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### Probability of significant result in a second sample given first was significant

It's an example mentioned in Amos Tversky and Daniel Kahneman's Belief in the Law of Small Numbers: Suppose you have run an experiment on 20 subjects, and have obtained a significant result which ...
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### Test if two normally distributed random variables have the same mean

We have two independent random variables which follow normal distributions $X_1\sim \mathcal N(\mu_1,\sigma_1)$, $X_2\sim \mathcal N(\mu_2,\sigma_2)$. From the context, we have that $\mu_1\leq\mu_2$. ...
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### Power of a test in testing of hypothesis

Power in testing of hypothesis is defined as the probability of making the correct decision. Then why do text books describe power=1-P(type 2 error) and not 1-P(type 1 error)
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### hypotheses testing [duplicate]

so I'm new to statistics and am not very comfortable with it yet. It may be a very simple question, but I'm finding this very difficult to understand In research papers the hypotheses are mostly in a ...
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### How can we reject null hypothesis based on p-values? [closed]

In textbook statistical tests, we usually calculate the probability of observing the data we observed given that the null hypothesis is true, i.e. $P[D|H_0]$. If this probability is small (e.g. \$<0....
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### What basis should be used to devize a significance/hypothesis test?

I am trying to understand the basis of hypothesis testing and I came up with a paradox. Let me explain with an example. Consider the case of trying to determine whether is coin is fair. The null ...