Question

widow's peak dominant(W) not having widow's peak(w)

sample size of 30 kids 15 have widow's peak and 15 did not

expected frequency of widow's peak is 75% chance of getting it and a 25% chance of not getting it

Perform Chi-square analysis to see if the data above agrees with the predicted outcome

Answer 1

Step 1:

Ho: Proportions of dominant widow's peak PDom = 0.75 and no widow's peak Pnopeak= 0.25

Ha: Some of the population proportions differ from the values stated in the null hypothesis

This corresponds to a Chi-Square test for Goodness of Fit.

Step 2: Test statistics

Widows peak	Observed values (fo)	Expected Proportions	Expected values (fe)	(fo-fe)2/ fe
Dominant	15	0.750	22.50	2.500
No widows peak	15	0.250	7.50	7.500
Total	30	1.000	30.00	10.000

= 10.00 (sum of last coloumn)

Step 3:

As the level of significance is not given, we will take = 0.05

Chi square critical = CHISQ.INV.RT(probability,df) = CHISQ.INV.RT (0.05, 1) = 3.841

As the ( 10.00) is greater than ciritical, we reject the Null hypothesis.

Hence we have sufficient evidence to believe that some of the population proportions differ from the values stated in the null hypothesis.