Question

For the z test, if sigma is unknown and n ≥ 30, one can substitute for sigma Select one:

a. chisquare
b. t
c. s
d. n

Answer 1

In a z-test with a sample size greater than or equal to 30 and unknown population standard deviation, the sample standard deviation (s) can be used as a substitute for sigma.

Step-by-step explanation:

For the z-test, if the population standard deviation (sigma) is unknown and the sample size (n) is greater than or equal to 30, one can substitute sigma with the sample standard deviation (s). This is because with larger sample sizes, the distribution of the sample mean will tend to be normally distributed according to the Central Limit Theorem, allowing the use of s as an estimate for sigma in the calculation of the test statistic. When the population standard deviation is unknown and the sample size is smaller than 30, the t-distribution should be used with degrees of freedom (df) equal to n - 1. However, for sample sizes larger than 30, the normal approximation to the Student's t-distribution is considered to be acceptable.