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 unformly distributed To test ths daim you randomly select 98 mothers who currently receive food stamps and record the educational attainment of each, The resuts are shown in Response the table on the nght A1 Frequency ot a high school graduale schod gadu re 0.025, can you reject the claim that the distroulion is uniform? Complete pats (al through (d 34 36 25 below (a) State Ho and H, and identity the ciam. Ho: The distnibution of educatianal attainment responses is H. The distribution of educational attainment responses is L Which hypothesis is the dlaim? (b) Decermine the critical vaue o and the rejection region Xo "L(Round to three deomal places as needed) Choose the correct rejection region belaw (c) Calculate the test statistic -L(Round to three deciral places as needed) (d) Decide whether to reject or fai to reject the nul hypothesis. Then interpret the decisian in the conmext of the criginad ckaim ' nan entres nsea o enough evidence i reject te cam hal te dst son red Ho u a 2.5% significance level there uniform.

Explanation / Answer

(a) H0 : The distriubtion of educational attainment responses is Uniform.

Ha : The distriubtion of educational attainment responses is not uniform.

Here alternative hypothesis is the claim.

(b) Here Criticla value of Chi - square is dF = 2 and alpha = 0.025

X2 0 = 7.378

Here rejection region

X2 > X2 0

Observed and expected table

Here expected frequency = 96/3 = 32

HEre X2 = 1.750

(d) Not reject H0 ; at a significance level, there is not enough evidence to reject the claim that the distribution of educational attainment resonenses is uniform.

Response Frequency(O) Expected (E) (O- E)^2/E Not high school graduate 34 32 0.125 Hig schol gradute 36 32 0.5 Colllege 26 32 1.125 sum 1.75

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