In one state, 52% of the voters are Republicans, and 48% are Democrats. In a second state, 47% of the
voters are Republicans, and 53% are Democrats. Suppose a simple random sample of 100 voters are
surveyed from each state.
What is the probablity that the sunvey will show a greater percentage of Republican voters in the second
state than in the first state?
(A) 0.04
(B) 0.05
(C) 0.24
(D) 0.71
E) 0.76
Answers
Given : In one state, 52% of the voters are Republicans, and 48% are Democrats. In a second state, 47% of the voters are Republicans, and 53% are Democrats. Suppose a simple random sample of 100 voters are
surveyed from each state.
To Find : probability that the survey will show a greater percentage of Republican voters in the second state than in the first state
Solution:
Mean Difference in number of republican in both states = 0.52 - 0.47 = 0.05
standard deviation = √ ((0.52)(0.48)/100 + (0.47)(0.53)/100 )
= 0.0706
Z score = ( Value - mean ) / SD
Difference should be less than 0 for greater percentage of Republican voters in the second state than in the first state
Hence Value = 0
=>Z = ( 0 - 0.05)/ 0.0706
=> Z = -0.708
From Z score table -0.708 refers to 0.24
Hence 0.24 is the probability that the survey will show a greater percentage of Republican voters in the second state than in the first state
Learn More:
In a survey of 400 youngsters aged 16-20 years,it was found that ...
https://brainly.in/question/8646957
A nationwide survey showed that 65‚ÑÖ of all cldren in Del ,dislike ...
https://brainly.in/question/3066837
