A social service organization reports that the level of educational attainment o

Question

A social service organization reports that the level of educational attainment of mothers receiving food stamps is uniformly distributed. To test this claim, you randomly select 95

mothers who currently receive food stamps and record the educational attainment of each. The results are shown in the table on

alpha equals 0.01

Response

Frequency, f

Not a high school graduate

3333

High school graduate

4040

College (1 year or more)

2222

(a) State

H 0

Ha

and identify the claim.

The distribution of educational attainment responses is uniform/not uniform

.Ha:

The distribution of educational attainment responses is

uniform

not uniform

.

Which hypothesis is the claim?

(b) Determine the critical value, and the rejection region.

(Round to three decimal places as needed.)

Choose the correct rejection region below.

A.

22

B.

220

C.

2>2

D.

2<20

(c) Calculate the test statistic.

(Round to three decimal places as needed.)

(d) Decide whether to reject or fail to reject the null hypothesis. Then interpret the decision in the context of the original claim.

Reject

Fail to reject

At a

11%

significance level, there

is not

is

enough evidence to reject the claim that the distribution of educational attainment responses

is

is not

uniform.

A social service organization reports that the level of educational attainment of mothers receiving food stamps is uniformly distributed. To test this claim, you randomly select 95

mothers who currently receive food stamps and record the educational attainment of each. The results are shown in the table on

the right. At

alpha equals 0.01

can you reject the claim that the distribution is uniform? Complete parts (a) through (d) below.

Response

Frequency, f

Not a high school graduate

3333

High school graduate

4040

College (1 year or more)

2222

Explanation / Answer

Ans:

1. State the null and alternate hypothesis Let H0 = The distribution is uniform and Ha = The distribution is not uniform alpha = 0.01 2. State the decision rule Critical value of the chi-square corresponding to dof = 3 - 1 = 2 and alpha = 0.01 is 9.2103 Reject H0 if the chi-square value obtained > 9.2103 3. Compute the value of the test statistic. Education Level Number of mothers (Recorded) Number of mothers (Expected) (Recorded - Expected)^2 (Recorded - Expected)^2 / Expected Not a High School Graduate 33 31.67 1.78 0.0561 High School Graduate 40 31.67 69.44 2.1930 College (1 Year or More) 22 31.67 93.44 2.9509 Total 95 95 Chi-square = 5.2000 4. What is the decision.  Interpret the results. Since the test value of the chi-square (5.2) < the critical value (9.2103), we fail to reject H0. There is not enough evidence to reject the claim that the distribution is uniform.

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