As part of the study on ongoing fright symptoms due to exposure to horror movies

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:

(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 = 0.01.)

Null Hypothesis:

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

Alternative Hypothesis:

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

State the 2 statistic and the P-value. (Round your answers for 2 and the P-value to three decimal places.)

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.   

     Waking
symptoms Bedtime symptoms Yes      No Yes 36 34 No 33 16

Explanation / Answer

a)percent of the students have lasting waking-life symptoms =(36+33)*100/119=57.98%

b)  percent of the students have both waking-life and bedtime symptoms =(36/119)*100 =30.25%

c)H0: There is no relationship between waking and bedtime symptoms

Ha: There is a relationship between waking and bedtime symptoms

applying chi square test:

2 =2.998

df =(row-1)*(column-1) =(2-1)*(2-1) =1

p value =0.0834

as p value is greater than 0.01 level

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

Observed Oi <20 20-39 Total liked 36 34 70 disliked 33 16 49 Total 69 50 119 Expected Ei=row*column/total <20 20-39 Total liked 40.588 29.412 70 disliked 28.412 20.588 49 Total 69 50 119 chi square =(Oi-Ei)2/Ei <20 20-39 Total liked 0.5187 0.7158 1.234 disliked 0.7410 1.0225 1.763 Total 1.260 1.738 3.00

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