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		35		33
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 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: Bedtime symptoms cause waking symptoms.H₀: There is no relationship between waking and bedtime symptoms.     H₀: Waking symptoms cause bedtime symptoms.H₀: There is a relationship between waking and bedtime symptoms.

Alternative Hypothesis:

H_a: There is a relationship between waking and bedtime symptoms.H_a: Waking symptoms cause bedtime symptoms.     H_a: Bedtime symptoms cause waking symptoms.H_a: There is no 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

a)

percent of the students have lasting waking-life symptoms =(68/119)*100=57.14%

b)

percent of the students have both waking-life and bedtime symptoms =(35/119)*100=29.41%

c)

H₀: There is no relationship between waking and bedtime symptoms.

H_a: There is a relationship between waking and bedtime symptoms.

applying chi square test:

Oi	Yes	No	Total
Yes	35	33	68
No	33	18	51
total	68	51	119
Ei=row total*column total/grand total	Yes	No	Total
Yes	38.86	29.14	68
No	29.14	21.86	51
total	68	51	119
=(Oi-Ei)2/Ei	Yes	No	Total
Yes	0.383	0.511	0.893
No	0.511	0.681	1.191
total	0.893	1.191	2.0846

χ² statistic =2.085

df =1

p value =0.149

Conclusion: We do not have enough evidence to conclude that there is a relationship.