Question

1 - Which of the following statements is true regarding a 95% confidence interval? Assume numerous large samples are taken from the population.
a. In 95% of all samples, the sample proportion will fall within 2 standard deviations of the mean, which is the true proportion for the population.
b. In 95% of all samples, the true proportion will fall within 2 standard deviations of the sample proportion.
c. If we add and subtract 2 standard deviations to/from the sample proportion, in 95% of all cases we will have captured the true population proportion.
d. All of the above.

2. Which of the following is a correct interpretation of a 90% confidence interval?

a. 90% of the random samples you could select would result in intervals that contain the true population value.
b. 90% of the population values should be close to our sample results.
c. Once a specific sample has been selected, the probability that its resulting confidence interval contains the true population value is 90%.
d. All of the above statements are true.

3 - Which of the following statements is false?

a. Confidence intervals are always close to their true population values.
b. Confidence intervals vary from one sample to the next.
c. The key to constructing confidence intervals is to understand what kind of dissimilarity we should expect to see in various samples from the same population.
d. None of the above statements are false

Answer 1

1.) b - Since, we never know the true population values, so sampling distribution plays a very crucial role.Confidence interval is constructed using sample observations. 95% CI means that out of all the samples possible, 95% samples are such that true population proportion lies within this interval

2.) a - As discussed above, 90% CI means that the out of all possible sample, 90% samples contain the true population proportion value within this interval

3.) Closeness is a relative term. CI depends on the level of significance ( aplha ). In first case alpha is 0.05 and 0.1. Higher the alpha, wider would be the length of confidence interval. Therefore, CI may or may not close to the true population values