Question

You may need to use the appropriate technology to answer this question.

Test the following hypotheses by using the

χ²

goodness of fit test.

H0:	pA = 0.40, pB = 0.40, and pC = 0.20
Ha:	The population proportions are not pA = 0.40, pB = 0.40, and pC = 0.20.

A sample of size 200 yielded 80 in category A, 20 in category B, and 100 in category C. Use α = 0.01 and test to see whether the proportions are as stated in

H₀.

(a)

Use the p-value approach.

Find the value of the test statistic.

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

p-value =

State your conclusion.

Reject H₀. We conclude that the proportions are equal to 0.40, 0.40, and 0.20.Reject H₀. We conclude that the proportions differ from 0.40, 0.40, and 0.20.     Do not reject H₀. We cannot conclude that the proportions differ from 0.40, 0.40, and 0.20.Do not reject H₀. We cannot conclude that the proportions are equal to 0.40, 0.40, and 0.20.

(b)

Repeat the test using the critical value approach.

Find the value of the test statistic.

State the critical values for the rejection rule. (If the test is one-tailed, enter NONE for the unused tail. Round your answers to three decimal places.)

test statistic ≤test statistic ≥

State your conclusion.

Do not reject H₀. We cannot conclude that the proportions are equal to 0.40, 0.40, and 0.20.Do not reject H₀. We cannot conclude that the proportions differ from 0.40, 0.40, and 0.20.     Reject H₀. We conclude that the proportions are equal to 0.40, 0.40, and 0.20.Reject H₀. We conclude that the proportions differ from 0.40, 0.40, and 0.20.

Answer 1

For the given Hypotheses:

H0:	pA = 0.40, pB = 0.40, and pC = 0.20
Ha:	The population proportions are not pA = 0.40, pB = 0.40, and pC = 0.20.

P-value approach:

The test statistic is calculated by tabulating the value as:

Chi Square=135

The P-value computed using Chi square table at Degree of freedom=3-1=2 as

The p-value is < 0.00001.

# Conclusion:

Reject H₀. We conclude that the proportions differ from 0.40, 0.40, and 0.20. Since P-value<<<0.01

b) The critical value approach:

THe test Statistic is the same as calculated above as 135

# Rejection region:

# Conclusion:

SInce test statistic >>>9.21 hence Reject H₀. We conclude that the proportions differ from 0.40, 0.40, and 0.20.

The chi square table for P-value compuation and rejection region computaion is shown below as: