A rearcher suspects that a higher proportion of teenaged girls than teenage boys

Question

A rearcher suspects that a higher proportion of teenaged girls than teenage boys do not eat breakfast on a regular basis. a random sample of 200 teenageg girls show that 80 do not eat breakfast on a regular basis, whereas a sample of 150 teenaged boys showed 45 do not eat breakfast ona regular basis.

At the 1% significance level, can it be concluded that a higher proportion of teenaged girls do not eat breakfast on a regular basis? Formulate and test the appropriate hypothesis. Use the critical value approach

Explanation / Answer

We use the chi-squared approach and test the hypothesis individually fo girls and boys.

For girls, Ho : Higher proportion of girls don't eat breakfast on a regular basis

H1 : Lesser number eat the breakfast regularly

accept Ho if |chi| > chi at the given significance level.

Test statistic :

(120-100)^2 / 100 + (80-100)^2 / 100 = 8

[ chi ] @ 0.01% = 6.63

Thus, We have no reason to reject the hypothesis.

hence, it can be said that a large proportion of girls don't eat their breakfast regularly.

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