You would like to construct a 90% confidence interval to estimate the population 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 502 and a standard deviation of 75 . (a) What is the best point estimate, based on the sample, to use for the population mean?           (b) For each of the following sampling scenarios, determine which distribution should be used to calculate the critical value for the 90% confidence interval for the population mean.   (In the table, Z refers to a standard normal distribution, and t refers to a t distribution.)         Sampling scenario Z t Could use either Z or t Unclear The sample has size 80 , and it is from a non-normally distributed population with a known standard deviation of 75 .         Z t       The sample has size 85 , and it is from a non-normally distributed population.         Z t       The sample has size 20 , and it is from a normally distributed population with an unknown standard deviation.         Z t

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You would like to construct a
90%
confidence interval to estimate the population 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
502
and a standard deviation of
75
.

(a) What is the best point estimate, based on the sample, to use for the population mean?

 
 
 
 
 

(b) For each of the following sampling scenarios, determine which distribution should be used to calculate the critical value for the

90%
confidence interval for the population mean.

 

(In the table, Z refers to a standard normal distribution, and

t
refers to a t distribution.)

 

 
 
 
Sampling scenario Z
t
Could use either
Z
or
t
Unclear
The sample has size
80
, and it is from a non-normally distributed population with a known standard deviation of
75
.
 
 
 
 
Z
t
 
 
 
The sample has size
85
, and it is from a non-normally distributed population.
 
 
 
 
Z
t
 
 
 
The sample has size
20
, and it is from a normally distributed population with an unknown standard deviation.
 
 
 
 
Z
t
 
 
 
 
 
 
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