Select which correctly describe the 95% confidence interval. (Select all that apply.) 95 employees have heights in this interval. 95% of employees have heights in this interval. We are 95% confident that the mean height of the entire business is larger than this interval. We are 95% confident that the mean height of the entire business is in this interval. We are 5% confident that the mean height of the entire business is in this interval. The 85% confidence interval is a subset of the 95% confidence interval. The upper height represents the 95th percentile. The 95% confidence interval is a subset of the 85% confidence interval.

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Answer:

Correct option:

"We are 95% confident that the mean height of the entire business is in this interval."

Step-by-step explanation:

The (1 - α)% confidence interval for population parameter implies that there is a (1 - α) probability that the true value of the parameter is included in the interval.

Or, the (1 - α)% confidence interval for the parameter implies that there is        (1 - α)% confidence or certainty that the true parameter value is contained in the interval.

Assume that the 95% confidence interval for the mean height of the entire business is, (p₁, p₂).

The 95% confidence interval for the mean height of the entire business implies that:

  • We are 95% confident that the true mean height of the entire business is in this interval.
  • There is a 0.95 probability that the true means lies in this interval.
  • If 100 such interval are computed using 100 samples of the same size, then 95 of those intervals will consist of the true mean height.
  • The upper height of a 95% confidence interval represents the 97.5th percentile and the lower height represents the 2.5th percentile.

Thus, the correct option is:

"We are 95% confident that the mean height of the entire business is in this interval."