Question

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.

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