PORTAGE LEARNING MATH 110 MODULE 10 EXAM
- Find the value of X
2 for 17 degrees of freedom and an area of .005 in the right tail of the chi-square distribution.
Look across the top of the chi-square distribution table for .005, then look down the left column for 17.These two meet at X
2 =35.718.
- Find the value of X
- for 10 degrees of freedom and an area of .005 in the left tail of the chi-square distribution.
Since the chi-square distribution table gives the area in the right tail, we must use 1 - .005 = .995. Look across the top of the chi-square distribution table for .995, then look down the left column for 10. These two meet at X
2 =2.156.
- Find the value of X
- values that separate the middle 80 % from the rest of the distribution for 9 degrees of
freedom.
In this case, we have 1-.80=.20 outside of the middle or .20/2 = .1 in each of the tails.
Notice that the area to the right of the first X 2 is .80 + .10 = .90. So we use this value and a DOF of 9 to get X 2
= 4.168.
The area to the right of the second X 2 is .10. So we use this value and a DOF of 9 to get X 2
= 14.684.
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- Find the critical value of F for DOF=(4,17) and area in the right tail of .05
In order to solve this, we turn to the F distribution table that an area of .05. DOF=(4,17) indicates that degrees of freedom for the numerator is 4 and degrees of freedom for the denominator is 17. So, we look up these in the table and find that F=2.96.
- The mayor of a large city claims that 30 % of the families in the city earn more than $ 100,000 per year;
52 % earn between $ 30,000 and $ 100,000 (inclusive); 18 % earn less than $ 30,000 per year.In order to test the mayor’s claim, 285 families from the city are surveyed and it is
found that:
90 of the families earn more than $ 100,000 per year; 135 of the families earn between $ 30,000 and $ 100,000 per year (inclusive); 60 of the families earn less $ 30,000.
Test the mayor’s claim based on 5 % significance level.
We will set
H0: The mayor’s distribution is correct.
H1: The mayor’s distribution is not
correct.This is a multinomial experiment, for multinomial experiments, we use the chi-square distribution.Calculate the degrees of freedom for three possible outcomes: DOF=3-1=2. Our level of significance is 5% (.05). So look up DOF of 2 and .05 on the Chi-square distribution table to get
5.991.
For the expected frequencies, we will use Ei = npi. So, the expected frequencies (of the n=285 in
the sample) based on the mayor’s distribution:
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