1. Let X be a sample of size 10 of a pupolation and Y a sample of size 100 of the same population. About the confidence interval for the mean of this samples with the same significance level, it is correct to say:
- The confidence interval for the mean for the sample X is bigger than the confidence interval for the mean fot the sample Y.
- The confidence interval for the mean for the sample X is smaller than the confidence interval for the mean fot the sample Y.
- The confidence interval for the mean for the sample X is the same than the confidence interval for the mean for the sample Y.
- There isn't enough information to answer the question.
2. Suppose you have a sample of 100 heights of individuals from a specific population. For this question, let's assume the standard deviation of the population is 1 cm, You have found that the sample mean of these 100 individuals is 175 cm. Suppose you want to build a confidence interval with 99% of confidence level.
What expression describes the margin of error for this specific task?
- (A)
- (B)
- (C)
- (D)
3. To calculate one confidence interval for the mean of a population with unknown distribution, what assumptions we must assure (check all that apply)?
- The sample is a random sample.
- We can only have a confidence interval if the population is known as having a Normal distribution.
- If the distribution is not Normal, the sample size must be big enough (usually over 30).
- The sample must have mean 0 and standard deviation 1.
4. You have a sample of size 20 from a population with unknown mean and standard deviation. You measured that the sample mean
Hint:
-
$\left( 48.95, 51.05 \right)$ -
$\left( 45.32, 54.68 \right)$ -
$\left( 45.2, 54.8 \right)$ -
$\left( 48.9, 51.1 \right)$