Question

To test μ for an x distribution that is mound-shaped using sample size n ≥ 30, how do you decide whether to use the normal or Student's t distribution?

A.If σ is known, use the standard normal distribution. If σ is unknown, use the Student's t distribution with n – 1 degrees of freedom.
B. If σ is unknown, use the standard normal distribution. If σ is known, use the Student's t distribution with n – 1 degrees of freedom.
C. If σ is known, use the standard normal distribution. If σ is unknown, use the Student's t distribution with n degrees of freedom.
D. For large samples we always the standard normal distribution.

Answer 1

The correct option is A) If σ is known, use the standard normal distribution. If σ is unknown, use the Student's t distribution with n – 1 degrees of freedom.

Explanation:

Consider the provided information.

The t-distribution of the Student is a distribution of probability that is used when when the sample size is small and/or when the population variance is unknown to estimate population parameters.

The number of independent observations is equal to the sample size minus one when calculating a mean score or a proportion from a single sample.

Since µ and σ determine the shape of the distribution so we use standard normal distribution if σ is known.

Hence, the correct option is A) If σ is known, use the standard normal distribution. If σ is unknown, use the Student's t distribution with n – 1 degrees of freedom.