Question

Use the sample data below to test the hypotheses H0: p1 = p2 = p3 Ha:...

Use the sample data below to test the hypotheses

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

where

pi

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.

Homework Answers

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.

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