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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)

$$z_{0.01} \cdot \frac{1}{10}$$

  • (B)

$$z_{0.005} \cdot \frac{1}{100}$$

  • (C)

$$z_{0.005} \cdot \frac{1}{10}$$

  • (D)

$$z_{0.1} \cdot \frac{1}{100}$$

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 $\bar{X} = 50$ and the sample standard deviation is $s = 10$. A confidence interval of 95% of confidence level is given by:

Hint: $t_{0.025} = 2.093$

  • $\left( 48.95, 51.05 \right)$
  • $\left( 45.32, 54.68 \right)$
  • $\left( 45.2, 54.8 \right)$
  • $\left( 48.9, 51.1 \right)$