In: Math
Each person in a large sample of German adolescents was asked to
indicate which of 50 popular movies they had seen in the past year.
Based on the response, the amount of time (in minutes) of alcohol
use contained in the movies the person had watched was estimated.
Each person was then classified into one of four groups based on
the amount of movie alcohol exposure (groups 1, 2, 3, and 4, with 1
being the lowest exposure and 4 being the highest exposure). Each
person was also classified according to school performance. The
resulting data is given in the accompanying table.
Assume it is reasonable to regard this sample as a random sample of
German adolescents. Is there evidence that there is an association
between school performance and movie exposure to alcohol? Carry out
a hypothesis test using
α = 0.05.
Alcohol Exposure Group | |||||
---|---|---|---|---|---|
1 | 2 | 3 | 4 | ||
School Performance |
Excellent | 111 | 94 | 51 | 67 |
Good | 329 | 325 | 318 | 297 | |
Average/Poor | 239 | 259 | 312 | 319 |
State the null and alternative hypotheses.
H0: Alcohol exposure and school performance
are not independent.
Ha: Alcohol exposure and school
performance are independent. H0: The
proportions falling into the alcohol exposure categories are not
all the same for the three school performance groups.
Ha: The proportions falling into the
alcohol exposure categories are the same for the three school
performance groups. H0:
The proportions falling into the alcohol exposure categories are
the same for the three school performance groups.
Ha: The proportions falling into the
alcohol exposure categories are not all the same for the three
school performance groups. H0: Alcohol exposure
and school performance are independent.
Ha: Alcohol exposure and school
performance are not independent.
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?
Do not reject H0. There is not enough evidence to conclude that there is an association between alcohol exposure and school performance. Reject H0. There is convincing evidence to conclude that there is an association between alcohol exposure and school performance. Do not reject H0. There is not enough evidence to conclude that the proportions falling into the alcohol exposure categories are not all the same for the three school performance groups. Reject H0. There is convincing evidence to conclude that the proportions falling into the alcohol exposure categories are not all the same for the three school performance groups.
You may need to use the appropriate table in Appendix A to answer
this question.