A researcher wants to determine if the number of minutes spent watching televisi

Question

A researcher wants to determine if the number of minutes spent watching television per day is independent of gender. A random sample of 315 adults was selected and the results are shown below. Is there enough evidence to conclude that the number of minutes spent watching television per day is related to gender? Use =0.05.

38. A researcher wants to determine if the number of minutes spent watching television per day is independent of gender. A random sample of 315 adults was selected and the results are shown below. Is there enough evidence to conclude that the number of minutes spent watching television per day is related to gender? Use -0.05 Gender Minutes spent watching TV per day 0-3030 - 60 60 -90 90- over |Totals 35 45 80 75 45 120 180 15135 315 Male 25 45 Female 30 Totals 60 (a) State the conditions that must be met in order to perform this hypothesis test (b) State hypotheses (c) Perform the test and state the test used, the P-value, and the decision. (d) Write a conclusion in context using a complete sentence

Explanation / Answer

a) conditions to met is that data should be independent from each other as well expected frequency for each cell should be greater then 5.

b)

null hypothesis:Ho:  number of minutes spent watching television per day is independent to gender.

alternate hypothesis:Ha: number of minutes spent watching television per day is related to gender

c)pplying chi square test of independence on above data:

from abvoe test stat X2 =18.146

degree of freedom =(number of rows-1)*(number of columns-1) =(2-1)*(4-1) =3

for above degree of freedom and test stat ; p value =0.0004

as p value is very less we reject null hypothesis.

d) we have sufficient evidence to conclude that number of minutes spent watching television per day is related to gender

Observed O 0-30 30-60 60-90 90-over Total male 25 35 75 45 180 female 30 45 45 15 135 Total 55 80 120 60 315 Expected E=rowtotal*column total/grand total 0-30 30-60 60-90 90-over Total male 31.43 45.71 68.57 34.29 180 female 23.57 34.29 51.43 25.71 135 Total 55 80 120 60 315 chi square =(O-E)^2/E 0-30 30-60 60-90 90-over Total male 1.3149 2.5112 0.6027 3.3482 7.777 female 1.753 3.348 0.804 4.464 10.369 Total 3.068 5.859 1.406 7.813 18.146

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