Question

Suppose that we want to estimate the mean germination time of strawberry seeds. The germination times for the sample of strawberries we choose has a mean of 20 days and a standard deviation of 1.5 days. 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 either Z or Sampling Scenario unclear (1) The sample has size 13, and it is from a population with a distribution about which we know very little. (2) The sample has size 100, and it is from a non- normally distributed population with a known standard deviation of 1.4. (3) The sample has size 20, and it is from a normally distributed population with a known standard deviation of 1.4. (4) The sample has size 10, and it is from a normally distributed population with unknown standard deviation. (5) The sample has size 95, and it is from a non- normally distributed population.

Answer 1

correct option has been marked against each tab :

1) unclear ; since sample size is less than 30 and distribution is unknown

2) z ; since sample size is >30 and standard deviation is known

3)z , since standard deviation is known and distribution is normal

4) t since distribution is normal and standard deviation is unknown

5) could use either: since sample size is >30 and standard deviation is unknown

could use either Z or Sampling Scenario unclear (1) The sample has size 13, and it is from a population with a distribution about which we know Correct very little. (2) The sample has size 100, and it is from a non- normally distributed population with a known Correct standard deviation of 1.4. (3) The sample has size 20, and it is from a normally distributed population with a known Correct standard deviation of 1.4. (4) The sample has size 10, and it is from a normally distributed population with unknown Correct standard deviation. Correct (5) The sample has size 95, and it is from a non- normally distributed population.