Question

Use the sample data below to test the hypotheses

H0:	p1 = p2 = p3
Ha:	not all population proportions are equal

where

p_i

is the population proportion of Yes responses for population i.

Response	Populations
	1	2	3
Yes	155	155	86
No	105	155	94

Find the value of the test statistic. (Round your answer to three decimal places.)

Find the p-value. (Round your answer to four decimal places.)

p-value =

Using a 0.05 level of significance, state your conclusion.

Reject H₀. We cannot conclude that not all population proportions are equal.

Do not reject H₀. We conclude that not all population proportions are equal.     

Do not reject H₀. We cannot conclude that not all population proportions are equal.

Reject H₀. We conclude that not all population proportions are equal.

Answer 1

#observed frequency is

Response	1	2	3	Total
ye	155	155	86	396
No	105	155	94	354
total	260	310	180	750

#Expected Frequency

Ei=Σrow*Σcolumn/Σtotal

Expected	Response	1	2	3	Total
	ye	137.28	163.68	95.04	396
	No	122.72	146.32	84.96	354
	total	260		180	750

table for χ2= (Oi-Ei)2/Ei

	Respons	1	2	3	Total
	ye	2.287284382	0.46030303	0.85986532	3.607453
	No	2.558657106	0.514915254	0.961883239	4.035456
	total	4.845941488	0.975218285	1.821748559	7.642908

# test statistics=χ2= (Oi-Ei)2/Ei

=7.642

degrree of freedom =(r-1)*(c-1)=(2-1)*(3-1)=2

#P-value=0.024

#p-value is less than 0.05 we reject H0

#conclusion

Reject H₀. We conclude that not all population proportions are equal.