In a study of high-achieving high school graduates, the authors
of a report surveyed 834 high school graduates who were considered
"academic superstars" and 434 graduates who were considered "solid
performers." One question on the survey asked the distance from
their home to the college they attended.
Assuming it is reasonable to regard these two samples as random
samples of academic superstars and solid performers nationwide, use
the accompanying data to determine if it is reasonable to conclude
that the distribution of responses over the distance from home
categories is not the same for academic superstars and solid
performers. Use
α = 0.05.
Distance of College from Home (in miles) | |||||
---|---|---|---|---|---|
Student Group | Less than 40 |
40 to 99 |
100 to 199 |
200 to 399 |
400 or More |
Academic Superstars | 158 | 157 | 143 | 151 | 225 |
Solid Performers | 104 | 94 | 83 | 66 | 87 |
State the null and alternative hypotheses.
H0: The proportions falling into the
distance categories are not all the same for the two student
groups.
Ha: The proportions falling into the
distance categories are the same for the two student
groups.H0: Student group and distance of
college from home are independent.
Ha: Student group and distance of
college from home are not
independent. H0: Student
group and distance of college from home are not independent.
Ha: Student group and distance of
college from home are independent.H0: The
proportions falling into the distance categories are the same for
the two student groups.
Ha: The proportions falling into the
distance categories are not all the same for the two student
groups.
Calculate the test statistic. (Round your answer to two decimal
places.)
χ2 =
What is the P-value for the test? (Round your answer to
four decimal places.)
P-value =
What can you conclude?
Reject H0. There is convincing evidence to conclude that the proportions falling into the distance categories are not all the same for the two student groups.Do not reject H0. There is not enough evidence to conclude that the proportions falling into the distance categories are not all the same for the two student groups. Do not reject H0. There is not enough evidence to conclude that there is an association between student group and distance of college from home.Reject H0. There is convincing evidence to conclude that there is an association between student group and distance of college from home.
The statistical software output for this problem is :
Test statistics = 12.24
P-value = 0.0157
.Reject H0. There is convincing evidence to conclude that there is an association between student group and distance of college from home.
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