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.

Answer 1

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.