As part of the study on ongoing fright symptoms due to exposure to horror movies at a young age, the following table was presented to describe the lasting impact these movies have had during bedtime and waking life: Waking symptoms Bedtime symptoms Yes No Yes 36 33 No 34 16
(a) What percent of the students have lasting waking-life symptoms? (Round your answer to two decimal places.) %
(b) What percent of the students have both waking-life and bedtime symptoms? (Round your answer to two decimal places.) %
(c) Test whether there is an association between waking-life and bedtime symptoms. State the null and alternative hypotheses. (Use α = 0.01.)
Null Hypothesis:
H0: Waking symptoms cause bedtime symptoms.
H0: There is no relationship between waking and bedtime symptoms.
H0: There is a relationship between waking and bedtime symptoms.
H0: Bedtime symptoms cause waking symptoms.
Alternative Hypothesis:
Ha: Bedtime symptoms cause waking symptoms.
Ha: There is no relationship between waking and bedtime symptoms.
Ha: Waking symptoms cause bedtime symptoms.
Ha: There is a relationship between waking and bedtime symptoms.
State the χ2 statistic and the P-value. (Round your answers for χ2 and the P-value to three decimal places.)
χ2 =
df =
P =
Conclusion:
We do not have enough evidence to conclude that there is a relationship.
We have enough evidence to conclude that there is a relationship.
From the given data
Waking symptoms | Bedtime symptoms | Total | |
Yes | 36 | 33 | 69 |
No | 34 | 16 | 50 |
Total | 70 | 49 | 119 |
a) The percent of the students have lasting waking-life symptoms is 70/119 = 0.5882 = 58.8%
b) The percent of the students have both waking-life and bedtime symptoms (70/119) *(49/119) = 0.2422
c) H0: There is no relationship between waking and bedtime symptoms.
Ha: There is a relationship between waking and bedtime symptoms.
The expected frequencies are
Waking symptoms | Bedtime symptoms | Total |
40.588 | 28.412 | 69 |
29.412 | 20.588 | 50 |
70 | 49 | 119 |
The chi-square contribution values are
Oi | Ei | (Oi-Ei)^2 /Ei |
36 | 40.588 | 0.5186 |
33 | 28.412 | 0.7409 |
34 | 29.412 | 0.7157 |
16 | 20.588 | 1.0224 |
Total: | 2.9976 |
Test Statistic, X^2: 2.9979
Degrees of freedom: 1
P-Value: 0.0834
since P-value >alpha (=0.01) so we accept H0
Thus we conclude that We do not have enough evidence to conclude that there is a relationship.
As part of the study on ongoing fright symptoms due to exposure to horror movies at...
As part of the study on ongoing fright symptoms due to exposure to horror movies at a young age, the following table was presented to describe the lasting impact these movies have had during bedtime and waking Waking Symptoms Bedtime Symptoms Yes No Yes 36 32 No 33 18 (a) What percent of the students have lasting waking-life symptoms? (Round your answer to two decimal places.) ___% (b) What percent of the students have both waking-life and bedtime symptoms? (Round...
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