Question

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?

Paired t-testTwo sample proportion test    Chi-squared Test for Goodness of FitTwo sample t-test

b) Given that the standard error equals 0.0621, what is the value of the test statistic? (3 decimal places)

c) The p-value for the test was 0.0453. What could you say about a 95% confidence interval?

The interval would go from 0.5313 to 0.6557.0 would not be inside the confidence interval.    We would not be able to determine if 0 is or is not in the interval without first constructing the interval.0 would be inside the confidence interval.

Answer 1

Given

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.