Question

Solocting a distribution for inforences on the population mean Suppose that we want to estimate the number of holding penalties assessed during a college football game. The sample of games we pick has a mean of 3.4 penalties per game and a standard deviation of 0.7 penalties per game. 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 tdistribution.) could use either Z or Sarfgling Scenario unclear (1) The sample has size 11, and it is from a normally distributed population with a known standard deviation of 0.75. O (2) The sample has size 80, and it is from a non- normally distributed population O (3) The sample has sire 20, and it is from a normally distributed population with unknown standard deviation. (4) The sample has size 75, and it is from a non- normally distributed population with a known standard deviation of 0.75 O (5) The sample has size 13, and it is from a population with a distribution about which we know very little O

Answer 1

Solution:-

Sampling scenario
1)	z-test (Normally distributed and known population standard deviation)
2)	t-test (Not normally distributed and sample size is large enough)
3)	t-test (Normally distributed and unknown population standard deviation
4)	z-test (Known population standard deviation and sample size is greater than 30.)
5)	Unclear (Sample size is low and less information about population)