Question

Suppose that we want to estimate the mean score on a nationwide examination in psychology, and for this purpose we choose a random sample of exam scores The sample we choose has a mean of 516 and a standard deviation of 75 . For each of the following sampling scenarios, determine which test statistic is appropriate to use when making inference statements about the population mean (In the table, Z refers to a variable having a standard normal distribution, and t refers to a variable having a t distribution.) could use Sampling Scenario either Z or unclear t (1) The sample has size 90, and it is from a non- normally distributed population with a known standard deviation of 75 (2) The sample has size 15, and it is from a normally distributed population with a known standard deviation of 75 (3) The sample has size 100, and it is from a non normally distributed population (4) The sample has size 13, and it is from a normally distributed population with unknown standard deviation. (5) The sample has size 12, and it is from a population with a distribution about which we know very little. ? X

Answer 1

(1) z

>> As the sample size is large, the sampling distribution is approximately normal even the population distribution is non-normal.

(2) z

>> As the population standard deviation is known here and the population distribution is normal, we use z distribution.

(3) z

>> As the sample size is large, the sampling distribution is approximately normal even the population distribution is non-normal.

(4) t

>> As the sample size is small, the population distribution is normal and the population standard deviation is not known, we use t distribution.

(5) unclear

Population standard deviation known unknown sample size large n>30 small n<30 Z .Z 1 Zort t .