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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 103103
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 0.05 commaα=0.05, can you reject the claim that the distribution is uniform? Complete parts (a) through (d) below.	Response Frequency, f Copy to Clipboard + Open in Excel + Not a high school graduate 3636 High school graduate 4040 College (1 year or more) 2727

(a) State

Upper H 0H0

and

Upper H Subscript aHa

and identify the claim.

Upper H 0H0 :

The distribution of educational attainment responses is

▼

uniform

not uniform

.

Upper H Subscript aHa :

The distribution of educational attainment responses is

▼

uniform

not uniform

.

Which hypothesis is the claim?

Upper H 0H0

Upper H Subscript aHa

(b) Determine the critical value,

font size increased by 1 font size increased by 1 font size increased by 1 chi Subscript 0 Superscript 2χ20 ,

and the rejection region.

font size increased by 1 font size increased by 1 font size increased by 1 chi Subscript 0 Superscript 2χ20equals=nothing

(Round to three decimal places as needed.)

Choose the correct rejection region below.

A.

font size increased by 1 font size increased by 1 font size increased by 1 chi squared greater than font size increased by 1 font size increased by 1 font size increased by 1 chi Subscript 0 Superscript 2χ2>χ20

B.

font size increased by 1 font size increased by 1 font size increased by 1 chi squared less than or equals font size increased by 1 font size increased by 1 font size increased by 1 chi Subscript 0 Superscript 2χ2≤χ20

C.

font size increased by 1 font size increased by 1 font size increased by 1 chi squared less than font size increased by 1 font size increased by 1 font size increased by 1 chi Subscript 0 Superscript 2χ2<χ20

D.

font size increased by 1 font size increased by 1 font size increased by 1 chi squared greater than or equals font size increased by 1 font size increased by 1 font size increased by 1 chi Subscript 0 Superscript 2χ2≥χ20

(c) Calculate the test statistic.

font size increased by 1 font size increased by 1 font size increased by 1 chi squaredχ2equals=nothing

(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

Upper H 0H0.

At a

55 %

significance level, there

▼

is

is not

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

▼

is not

is

uniform.

Answer 1

This is hypothesis test is chi-square test of goodness of fit. We use this test when we have been given a data and we assumed that the frequencies follows some predetermined distribution. We want to test this assumption and so we collect some data and compare and see if there is any difference between the distributed and the actual values.

We have been given some observed frequencies, null hypothesis assume that the frequencies are uniform that means each category is expected to have the same frequencies.

Stating the hypothesis

(1)

: The distribution of educational attainment responses is uniform

VS

: The distribution of educational attainment responses is not uniform

The claim is the . (This is mentioned in the question whether we reject the claim that the distribution is uniform)

(2) Critical value at 0.05

= (n = no. of categories)

= 5.9915    (Using chi sq distribution tables with prob = 0.05, df = 2)

(3) To calculate test stat we need know the expected frequencies. Since there are 3 categories and we assume uniform dist, each expected freq = Total freq / 3

Response	Freq	Expected
Not a HS grad	3636	3467.666667	168.3333	8.171521
HS Grad	4040	3467.666667	572.3333	94.46278
College	2727	3467.666667	-740.667	158.2006
Total	10403	10403		260.835

Test Stat =

= 260.835

(4) Since Test Stat > Critical Value

We reject the as there is enough evidence to reject the claim that the distribution of educational attainment responses is uniform.