A university carried out a study that gives the age distribution for a representative sample of 375 Texas Lottery players.
Age Group |
Frequency |
|---|
from 18 to 24 |
7 |
from 25 to 34 |
33 |
from 35 to 44 |
33 |
from 45 to 54 |
60 |
from 55 to 64 |
107 |
at least 65 |
135 |
Total
|
375
|
Using data from the U.S. Census Bureau† for 2014, the age distribution of adults in Texas was 14% between the age of 18 and 24, 20% between the age of 25 and 34, 19% between the age of 35 and 44, 18% between the age of 45 and 54, 14% between the age of 55 and 64, and 15% aged 65 or older. Is it reasonable to conclude that one or more of the age groups buys a disproportionate share of Texas Lottery tickets? Use a chi-square goodness-of-fit test with
? = 0.05.
(Hint: See Example 12.2.)
Letp
1,p
2,p
3,p
4,p
5, andp
6 be the proportions of lottery ticket purchasers in the different age groups.
State the null and alternative hypotheses.
H
0:p
1 =p
2 =p
3 =p
4 =p
5 =p
6 = 17
H
a
:H
0 is not true.H
0:p
1 = 0.14,p
2 = 0.2,p
3 = 0.19,p
4 = 0.18,p
5 = 0.14,p
6 = 0.15
H
a
:H
0 is not true.H
0:p
1 =p
2 =p
3 =p
4 =p
5 =p
6 = 0.17
H
a
:H
0 is not true.H
0:p
1 = 52.5,p
2 = 75,p
3 = 71.25,p
4 = 67.5,p
5 = 52.5,p
6 = 56.25
H
a
:H
0 is not true.H
0:p
1 = 14,p
2 = 20,p
3 = 19,p
4 = 18,p
5 = 14,p
6 = 15
H
a
:H
0 is not true.
Calculate the test statistic. (Round your answer to two decimal places.)
?2 =
Use technology to calculate theP-value. (Round your answer to four decimal places.)
P-value =
What can you conclude?
Fail to rejectH
0. We have convincing evidence that one or more of the age groups buys a disproportionate share of Texas Lottery tickets.Fail to rejectH
0. We do not have convincing evidence that one or more of the age groups buys a disproportionate share of Texas Lottery tickets. RejectH
0. We do not have convincing evidence that one or more of the age groups buys a disproportionate share of Texas Lottery tickets.RejectH
0. We have convincing evidence that one or more of the age groups buys a disproportionate share of Texas Lottery tickets.