Question

You

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 96 mothers who currently receive food stamps and record the
educational attainment of each. The results are shown in the table on the right. At
a=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 33
High school graduate 38
College (1 year or more) 25
a) Determine the critical value, X
2
0 , and the rejection region.

Answer 1

a) The claim is generally represented by \(H_₀\), which states that the distribution is uniform.

b) The correct rejection region is:
`\(Z^2 \geq Z_0^2\)`

(a) **State H₀ and Hₐ and Identify the Claim:**

`\(H_0\)` : The distribution of educational attainment responses is uniform among mothers receiving food stamps.

Hₐ: The distribution of educational attainment responses is not uniform among mothers receiving food stamps.

The claim is generally represented by \(H_₀\), which states that the distribution is uniform.

a.
`\(H_0\)`

(b) **Determine the Critical Value,
`\(Z_0^2\)`, and the Rejection Region:**

Given that the significance level
`(\(\alpha\))` is 0.01, you need to find the critical value
`\(Z_0^2\)` from the chi-square distribution table with degrees of freedom df = k - 1, where k is the number of categories.

In this case, k = 3, so df = 2

After finding
`\(Z_0^2\)`, the correct rejection region is:

C.
`\(Z^2 \geq Z_0^2\)`

So, the decision rule would be to reject the null hypothesis
`(\(H_0\))` if the calculated chi-square test statistic
`(\(Z^2\))` is greater than or equal to the critical value
`\(Z_0^2\)`, indicating evidence against the claim of a uniform distribution of educational attainment among mothers receiving food stamps.

The probable question may be:

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 96 mothers who currently receive food stamps and record the educational attainment of each. The results are shown in the table on the right. At a 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 37

high school graduate 39

collage (1 year or more) 24

(a) State H_0 and H_a and identify the claim.

H_0: The distribution of educational attainment responses is

H_a: The distribution of educational attainment responses is

Which hypothesis is the claim?

a. H_0

b. H_a

(b) Determine the critical value, 7, and the rejection region.

Z_0^2=

Choose the correct rejection region below.

A. Z^2<Z_0^2

B. Z^2>Z_0^2

C. Z^2<=Z_0^2

D. Z^2<=Z_0^2