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One of the assumptions we sometimes need to make when performing statistical inferences is that the response variable in the population has a Normal distribution. Is it possible to check that this assumption is satisfied?

- No – we can’t really check this assumption since all data will look perfectly bell-shaped and symmetric, even if the population was not Normal.
- Yes – we can be absolutely sure the population was Normal if a plot of the data has no major outliers.
- No – we can’t really check this assumption since we don’t have the whole population, but the t distribution is robust to modest departures from Normality, so we can use it if a plot of the data has no major outliers.
- Yes – we can be absolutely sure the population was Normal if a plot of the data looks roughly bell-shaped and symmetric.
- Yes – we can be absolutely sure the population was Normal if a plot of the data looks perfectly bell-shaped and symmetric.

## Answer

The correct answer is: **No – we can’t really check this assumption since we don’t have the whole population, but the t distribution is robust to modest departures from Normality, so we can use it if a plot of the data has no major outliers.**

### What is Statistical Inference?

A common assumption made when doing statistical inferences is that the response variable in the population has a normal distribution. This assumption is important because many statistical procedures are based on normal distribution. When the response variable does not have a normal distribution, the results of the statistical procedure may be inaccurate.

### What is a Type I Error?

A type I error is when you conclude that there is a difference between two groups when there actually is no difference. For example, you may conclude that treatment A is better than treatment B when in reality they are both equally effective. The probability of making a type I error is denoted by alpha (α).

### What is a Type II Error?

A type II error is when you conclude that there is no difference between two groups when in reality there is a difference. For example, you may conclude that treatments A and B are equally effective when in reality, treatment A is better than treatment B. The probability of making a type II error is denoted by beta (β).

### What is the Power of a Statistical Test?

The power of a statistical test is the probability of correctly rejecting the null hypothesis when it is false. In other words, it’s the likelihood that you won’t make a type II error. The power of a test is affected by several factors, including:

- The size of the difference between the groups being compared (the larger the difference, the easier it will be to detect)
- The variability of the response variable (the more variable the responses are, the harder it will be to detect a difference)

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