Final answer:
Alpha (α) for a 90% confidence interval is 0.10, signifying a 10% chance that the confidence interval does not contain the population mean. This 10% is divided equally between the two tails of the normal distribution.
Step-by-step explanation:
When asked to find the 90% confidence interval of the mean, the value of α (alpha) is the probability that the confidence interval does not contain the unknown population parameter. In the context of a 90% confidence interval, α represents the proportion of probability left out in both tails of the normal distribution, which is 1 - 0.90 = 0.10 or 10%. Looking further into the details, this 10% is split equally between the two tails, hence α/2 = 5% in each tail. Therefore, the value of α when constructing a 90% confidence interval is 0.10.
The significance of α lies in its relationship with the confidence level and the interpretation of the confidence interval. If you were to repeat the sampling process many times, approximately 90% of the confidence intervals calculated from these samples would contain the true value of the population mean. This implies that there is a 10% chance (α) that any given confidence interval does not include the population mean.
When asked to find the 90% confidence interval of the mean, the value of α represents the significance level or the probability of Type I error. It is the probability that the confidence interval does not contain the true population mean. In this case, α is equal to 0.10 or 10% since the confidence interval excludes 10% of the data in the tails of the normal distribution.