MATH 110 Module 10 Exam
Question 1
pts
Find the value of X2 for 14 degrees of freedom and an area of .01 in the right tail of the chi-
square distribution. Your Answer:
X2=29.141
Solution. Look across the top of the chi-square distribution table for .01, then look down the left
column for 14. These two meet at X2 =29.141.
Question 2
pts
Find the value of X2 for 8 degrees of freedom and an area of .05 in the left tail of the chisquare
distribution. Your Answer:
1-.05=0.95
X2=2.733
Solution. Since the chi-square distribution table gives the area in the right tail, we must use 1 -
.05 = .95. Look across the top of the chi-square distribution table for .95, then look down the
left column for 8. These two meet at X2 =2.733.
Question 3
pts
Find the value of X2 values that separate the middle 80 % from the rest of the
distribution for 20 degrees of freedom. Your Answer:
1-.80=0.20 is outside of the middle .20/2 =0
.1 is in each of the tails
.80 + .10 = .90 X2 = 12.443
X2 is .10 X2 = 28.412
Solution. 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 X2 is .80 + .10 = .90. So we use this value and a DOF
of 20 to get X2 = 12.443.
The area to the right of the second X2 is .10. So we use this value and a DOF of 20 to get X2 =
28.412.
, Question 4
pts
Find the critical value of F for DOF=(3,10) and area in the right tail of .10. Your
Answer:
F=2.73
Solution. In order to solve this, we turn to the F distribution table that an area of .10.
DOF=(3,10) indicates that degrees of freedom for the numerator is 3 and degrees of freedom
for the denominator is 10. So, we look up these in the table and find that F=2.73.
Question 5
pts
You grandfather has been collecting pennies for many years. He has tens of thousands of
pennies in his basement. Your grandfather estimates that 20 % of the pennies have dates of
1900 and before, 25 % are dated between 1901 and 1940 (inclusive), 40 % are dated between
1941 and 1970 (inclusive), 15 % are dated after 1970. You test your grandfather’s claim and
randomly check 220 pennies. You find that 46 of the pennies have dates of 1900 and before, 53
are dated between 1901 and 1940 (inclusive), 79 are dated between 1941 and 1970 (inclusive),
42 are dated after 1970. Test your grandfather’s claim based on 5 % significance level. Your
Answer:
H0=Grandfathers estimated distribution is correct.
H1=Grandfather estimated distribution is incorrect.
4 possible outcomes so DF=3
Level of significance=5% =.05 Critical
value is 7.815
n=220
1900 and before E1=220(.20)=44
1901 to 1940 E2=220(.25)=55
1941 to 1970 E3=220(.40)=88 After
1970 E4=220(.15)=33
Observed frequencies:
1900 and before =46
1901 to 1940 =53
1941 to 1970 =79
After 1970 =42
X2=3.54
This is smaller than critical value 7.815 so we do NOT reject the null hypothesis. We will set
the null and alternate hypothesis:
H0: Your grandfather’s estimated distribution is correct.
H1: Your grandfather’s estimated distribution is not correct.
This is a multinomial experiment because it has more than two possible outcomes (there are
four possible outcomes). For multinomial experiments, we use the chi-square distribution.
Question 1
pts
Find the value of X2 for 14 degrees of freedom and an area of .01 in the right tail of the chi-
square distribution. Your Answer:
X2=29.141
Solution. Look across the top of the chi-square distribution table for .01, then look down the left
column for 14. These two meet at X2 =29.141.
Question 2
pts
Find the value of X2 for 8 degrees of freedom and an area of .05 in the left tail of the chisquare
distribution. Your Answer:
1-.05=0.95
X2=2.733
Solution. Since the chi-square distribution table gives the area in the right tail, we must use 1 -
.05 = .95. Look across the top of the chi-square distribution table for .95, then look down the
left column for 8. These two meet at X2 =2.733.
Question 3
pts
Find the value of X2 values that separate the middle 80 % from the rest of the
distribution for 20 degrees of freedom. Your Answer:
1-.80=0.20 is outside of the middle .20/2 =0
.1 is in each of the tails
.80 + .10 = .90 X2 = 12.443
X2 is .10 X2 = 28.412
Solution. 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 X2 is .80 + .10 = .90. So we use this value and a DOF
of 20 to get X2 = 12.443.
The area to the right of the second X2 is .10. So we use this value and a DOF of 20 to get X2 =
28.412.
, Question 4
pts
Find the critical value of F for DOF=(3,10) and area in the right tail of .10. Your
Answer:
F=2.73
Solution. In order to solve this, we turn to the F distribution table that an area of .10.
DOF=(3,10) indicates that degrees of freedom for the numerator is 3 and degrees of freedom
for the denominator is 10. So, we look up these in the table and find that F=2.73.
Question 5
pts
You grandfather has been collecting pennies for many years. He has tens of thousands of
pennies in his basement. Your grandfather estimates that 20 % of the pennies have dates of
1900 and before, 25 % are dated between 1901 and 1940 (inclusive), 40 % are dated between
1941 and 1970 (inclusive), 15 % are dated after 1970. You test your grandfather’s claim and
randomly check 220 pennies. You find that 46 of the pennies have dates of 1900 and before, 53
are dated between 1901 and 1940 (inclusive), 79 are dated between 1941 and 1970 (inclusive),
42 are dated after 1970. Test your grandfather’s claim based on 5 % significance level. Your
Answer:
H0=Grandfathers estimated distribution is correct.
H1=Grandfather estimated distribution is incorrect.
4 possible outcomes so DF=3
Level of significance=5% =.05 Critical
value is 7.815
n=220
1900 and before E1=220(.20)=44
1901 to 1940 E2=220(.25)=55
1941 to 1970 E3=220(.40)=88 After
1970 E4=220(.15)=33
Observed frequencies:
1900 and before =46
1901 to 1940 =53
1941 to 1970 =79
After 1970 =42
X2=3.54
This is smaller than critical value 7.815 so we do NOT reject the null hypothesis. We will set
the null and alternate hypothesis:
H0: Your grandfather’s estimated distribution is correct.
H1: Your grandfather’s estimated distribution is not correct.
This is a multinomial experiment because it has more than two possible outcomes (there are
four possible outcomes). For multinomial experiments, we use the chi-square distribution.
