QUESTION 22
Which one of the following is a correct statement about the probability distribution of a t random variable?
a. 
The mean is zero but the standard deviation is greater than 1. 

b. 
The mean and standard deviation can be any number. 

c. 
The mean is zero but the standard deviation is less than 1. 

d. 
The mean is zero and the standard deviation is 1. 
QUESTION 23
A professor finds that for 16 randomly selected students the time needed to complete an assignment had a sample mean of 66 minutes and a sample standard deviation of 40 minutes. If the time needed to complete the assignment is normally distributed, then the standard error of the mean is
a. 
5 

b. 
20 

c. 
16 

d. 
10 
QUESTION 24
A professor finds that for 16 randomly selected students the time needed to complete an assignment had a sample mean of 65 minutes and a sample standard deviation of 40 minutes. If we need to develop an interval estimate of the mean, the appropriate distribution to use is:
a. 
the Z distribution 

b. 
the t distribution 

c. 
the normal distribution 

d. 
none of the above 
Q.22 )
We know that when we have given the sample data from the given data we can calculate sample mean and sample standard deviation. So
b)The mean and standard deviation can be any number
Is correct answer.
Q.23)
n= 16 and sample standard deviation s= 40
We know that standard error = s/sqrt(n) = 40/4= 10
Hence d. 10 is correct answer.
Q.24)
Here we have given same size n, sample mean and sample standard deviation s.
We know that when population standard deviation is not given (unknown) then we use t distribution.
Here we have given sample standard deviation s and population standard deviation is not given hence we use t distribution.
Hence b) the t distribution is correct answer.
Hope this will help you. Thank you :)
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