Question

You would like to estimate the mean price of milk (per gallon) in your city. You select a random sample of prices from different stores. The sample has a mean of 3.75 dollars and a standard deviation of 0.21 dollars. 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 at distribution.) Sampling Scenario Z t could use either Zor undear E o 0 O o O (1) The sample has size 17, and it is from a normally distributed population with a known standard deviation of 0.30. (2) The sample has size 10, and it is from a population with a distribution about which we know very little (3) The sample has size 105, and it is from a non- normally distributed population with a known standard deviation of 0.30. (4) The sample has size 11 and it is from a normally distributed population with unknown standard deviation (5) The sample has size 110, and it is from a non- normally distributed population O e

Answer 1

Z tests are better to use when the normal distribution size is greater than 30, and the standard deviation is known. When the sample size is less than 30, and the standard deviation is not known then t test is used. We always prefer z test when the standard deviation is known.

1) Z test

As thr standard deviation is known to us.

2) Unclear

As the type of distribution we don't know.

3) Unclear

As the distribution is non normally distributed.

4) T test

As the sample size is less than 30, and standard deviation is not known of the normal distribution.

5) Unclear

As the distribution is non normally distributed.