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: Waking symptoms Bedtime symptoms Yes No 34 16 36 Yes No (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: Hg: Bedtime symptoms cause waking symptoms. Ho: There is no relationship between waking and bedtime symptoms. Ho: Waking symptoms cause bedtime symptoms Ho: There is a relationship between waking and bedtime symptoms. Alternative Hypothesis: Ha: Bedtime symptoms cause waking symptoms Ha: Waking symptoms cause bedtime symptoms. Hg: There is a relationship between waking and bedtime symptoms. Hg: 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.) x2 df= Conclusion: We have enough evidence to conclude that there is a relationship We do not have enough evidence to conclude that there is a relationship.

Explanation / Answer

Given table data is as below

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calculation formula for E table matrix

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expected frequecies calculated by applying E - table matrix formulae

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calculate chisquare test statistic using given observed frequencies, calculated expected frequencies from above

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set up null vs alternative as

null, Ho: no relation b/w bed time walking and Y OR bed time walking and Y are independent

alternative, H1: exists a relation b/w bed time walking and Y OR bed time walking and Y are dependent

level of significance, = 0.01

from standard normal table, chi square value at right tailed, ^2 /2 =6.6349

since our test is right tailed,reject Ho when ^2 o > 6.6349

we use test statistic ^2 o = (Oi-Ei)^2/Ei

from the table , ^2 o = 2.9979

critical value

the value of |^2 | at los 0.01 with d.f (r-1)(c-1)= ( 2 -1 ) * ( 2 - 1 ) = 1 * 1 = 1 is 6.6349

we got | ^2| =2.9979 & | ^2 | =6.6349

make decision

hence value of | ^2 o | < | ^2 | and here we do not reject Ho

^2 p_value =0.0834

ANSWERS

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a.
students have lasting waking life symtoms = 69/119 = 0.5798

b.
students having walking and bed time symtoms = 36/119 = 0.3025

c.

null, Ho: no relation b/w bed time walking and Y OR bed time walking and Y are independent

alternative, H1: exists a relation b/w bed time walking and Y OR bed time walking and Y are dependent

test statistic: 2.9979

critical value: 6.6349

p-value:0.0834

decision: do not reject Ho

we don't have enough evidence to conclude that there is a relationship

MATRIX col1 col2 TOTALS row 1 36 34 70 row 2 33 16 49 TOTALS 69 50 N = 119

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