Suppose that we want to estimate the mean score on a nationwide examination in anthropology, and for this purpose we choose a random sample of exam scores. The sample we choose has a mean of  492  and a standard deviation of  79  . 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.)   Sampling Scenario Z t could use either Z or t unclear (1) The sample has size 75, and it is from a non-normally distributed population.                 (2) The sample has size 17, and it is from a normally distributed population with unknown standard deviation.                 (3) The sample has size 80, and it is from a non-normally distributed population with a known standard deviation of 75.                 (4) The sample has size 19, and it is from a population with a distribution about which we know very little.                 (5) The sample has size 18, and it is from a normally distributed population with a known standard deviation of 75.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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Suppose that we want to estimate the mean score on a nationwide examination in anthropology, and for this purpose we choose a random sample of exam scores. The sample we choose has a mean of 
492
 and a standard deviation of 
79
 . 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.)

 

Sampling Scenario Z t could use either Z or t unclear
(1) The sample has size 75, and it is from a non-normally distributed population.
 
 
 
 
 
 
 
 
(2) The sample has size 17, and it is from a normally distributed population with unknown standard deviation.
 
 
 
 
 
 
 
 
(3) The sample has size 80, and it is from a non-normally distributed population with a known standard deviation of 75.
 
 
 
 
 
 
 
 
(4) The sample has size 19, and it is from a population with a distribution about which we know very little.
 
 
 
 
 
 
 
 
(5) The sample has size 18, and it is from a normally distributed population with a known standard deviation of 75.
 
 
 
 
 
 
 
 
 
 
 
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