Explain why use the word \"confidence\" when interpreting confidence intervals o

Question

Explain why use the word "confidence" when interpreting confidence intervals of "probability" Explain the relationship between the confidence level (1-alpha) and the width of the interval. Why don't we always compute 100% confidence intervals? Explain the relationship between the probability of type I errors and probability of type II errors why can't choose rejection regions that minimize both probabilities simultaneously. Assume that the sample size is fixed. Explain what a p value is, How do we p. values?

Explanation / Answer

Question 1:

The X % confidence interval just means that we could be X% sure that the true population parameter value would lie in that interval, therefore an X% confidence interval means that the probability of the true parameter to lie in that confidence interval is X/100 .

For example if we are computing a 95% confidence interval for the true population mean, we can say that the probability of the true population mean to lie in that interval would be 0.95.

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