In 1000 samples, assuming that the null hypothesis is true, how many times would you expect to commit Type I error if alpha=.05?
To determine the number of times you would expect to commit a Type I error in 1000 samples, assuming the null hypothesis is true and the significance level (alpha) is 0.05, you need to apply the concept of statistical significance.
A Type I error occurs when you reject the null hypothesis when it is actually true. In hypothesis testing, the significance level represents the maximum probability of committing a Type I error. In this case, alpha is set to 0.05, meaning you are willing to accept a 5% chance of committing a Type I error.
To calculate the expected number of Type I errors in 1000 samples, you can multiply the significance level (alpha) by the number of samples.
Expected number of Type I errors = alpha * number of samples
In this case, the calculation would be:
Expected number of Type I errors = 0.05 * 1000 = 50
So, if the null hypothesis is true and you conduct 1000 samples, you would expect to commit approximately 50 Type I errors.
It's important to note that this calculation assumes that the data follows a specific distribution under the null hypothesis. The actual number of Type I errors may deviate from this expectation due to randomness and sample variability.