A high school teacher once claimed that "Young men and young women don't fall in love at the same rate." Later in life, one of her students elected to test that. In cooperation with high schools in the Athens area, he took random samples of 128 17-year-old girls and 122 17-year-old boys and asked them "Do you believe you have experienced romantic love?" 68 of the girls believed they had; 80 of the boys believed they had. a) What test would be appropriate here? b) Given that the standard error equals 0.0621, what is the value of the test statistic?

Question

Emilee Hatfield

Mathematics

23 February, 03:03

A high school teacher once claimed that "Young men and young women don't fall in love at the same rate." Later in life, one of her students elected to test that. In cooperation with high schools in the Athens area, he took random samples of 128 17-year-old girls and 122 17-year-old boys and asked them "Do you believe you have experienced romantic love?" 68 of the girls believed they had; 80 of the boys believed they had. a) What test would be appropriate here? b) Given that the standard error equals 0.0621, what is the value of the test statistic?

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Heath Carey · Answer 1

Answer:Girls.

n1=128

x1=68

p1=x1/n1

=68/128

=0.5313

Boys

n2=122

x2=80 0.

p2=x2/n2 = 80/122 = 0.6557

A) Appropriate test to compare the this is 2 sample proportion test

B) S. E. = 0.0621

Test statistic

Z = (p1 - p2) / S. E.

= (0.5313 - 0.6557) / 0.0621

Z = - 2.003

C) p-value = 0.0453

For 95%confidence interval we can say that,

0 would not be in the confidence interval.

Becouse p-value < 0.05

Hence we reject the null hypothesis that is proportions are equal.