The authors of a paper concluded that more boys than girls listen to music at hi

Question

The authors of a paper concluded that more boys than girls listen to music at high volumes. This conclusion was based on data from independent random samples of 770 boys and 745 girls from a country, age 12 to 19. Of the boys, 397 reported that they almost always listen to music at a high-volume setting. Of the girls, 331 reported listening to music at a high-volume setting. Do the sample data support the authors' conclusion that the proportion of the country's boys who listen to musk: at high volume is greater than this proportion for the country's girls? Test the relevant hypotheses using a 0.01 significance level. (Use a statistical computer package to calculate the P-value. Use Round your test statistic to two decimal places and your P-value to four decimal places.)

Explanation / Answer

Null Hypothesis:

H0:p1=p2

p1=proportion of boys listening to music at high volume

p2=proportion of girls listerning to music at hgh volume

Alternative Hypothesis:

H1:p1>p2

level of significance=0.01

using R

Z.prop function calculates the value of Z, receiving input the number of successes (x1 and x2), and the total number of games (n1 and n2). We apply the function just written with the data of our problem:

Code is:

z.prop = function(x1,x2,n1,n2){
numerator = (x1/n1) - (x2/n2)
p.common = (x1+x2) / (n1+n2)
denominator = sqrt(p.common * (1-p.common) * (1/n1 + 1/n2))
z.prop.ris = numerator / denominator
return(z.prop.ris)
}
z.prop (397,331,770,745)

Output

Z=2.78

Z to p vlaue

The P-Value is 0.0027

The result is significant at p < 0.01.

Reject Null hypothesis

Accep[t ALternative Hypothesis

COnclusion:

There is statistical eviudence at 1% level of sginficance to support the claim that boys listen to high volume more than girls.

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