You'd like to estimate the proportion of the 12,152 full-time undergraduate students at a university who are foreign students.
You poll a random sample of 50 students, of whom 7 are from foreign countries. Unknown to you, the proportion of all undergraduate students who are foreign students is 0.06. Let X denote a random variable for which x=1 denotes foreign students and x=0 denotes students from the U.S. Complete parts (a) through (c).
a. Describe the data distribution.
The data distribution consists of ( )1's (denoting a foreign student) and ( )0's (denoting a student from the U.S.).
b. Describe the population distribution.
The population distribution consists of the x-values of the population of 12,152 full-time undergraduate students at theuniversity, ( )% of which are 1's (denoting a foreign student) and ( )% of which are 0's (denoting a student from the U.S.).
c. Find the mean and standard deviation of the sampling distribution of the sample proportion for a sample of size 50.
The mean is ( )
The standard deviation is ( )(Round to four decimal places asneeded.)
Explain what this sampling distribution represents.
The sampling distribution represents the probability distribution of the ( ) proportion of foreign students in a random sample of ( )students. In thiscase, the sampling distribution is approximately normal with a mean of ( ) and a standard deviation of ( )
a) The data distribution consists of ( 7 )1's (denoting a foreign student) and ( 43 )0's (denoting a student from the U.S.).
b) The population distribution consists of the x-values of the population of 12,152 full-time undergraduate students at theuniversity, ( 6 )% of which are 1's (denoting a foreign student) and ( 94 )% of which are 0's (denoting a student from the U.S.).
c) The mean is ( 0.06 )
The standard deviation is ( 0.0336 )
The sampling distribution represents the probability distribution of the ( sample ) proportion of foreign students in a random sample of ( 50 ) students. In this case, the sampling distribution is approximately normal with a mean of ( 0.06 ) and a standard deviation of ( 0.0336 )
