A survey of 800 randomly selected recent degree recipients f

A survey of 800 randomly selected recent degree recipients found that 155 received associate degrees; 450 bachelor degrees; 20, first professional degrees; 160, master degrees; and 15, doctorates. Is there sufficient evidence to conclude that at least one of the proportion differs froma report which stated that 23.3% were associate degrees; 20.6%, master degrees; and 2%, doctorates? Use a=0.05

Solution

A survey of 800 randomly selected recent degree recipients found that 155 received associate degrees; 450 bachelor degrees; 20, first professional degrees; 160, master degrees; and 15, doctorates. Is there sufficient evidence to conclude that at least one of the proportion differs froma report which stated that 23.3% were associate degrees; 20.6%, master degrees; and 2%, doctorates? Use a=0.05

51.1% bachelors degree, 3% first professional degrees

Null hypothesis: All of the proportion are same as the   report proportions

Alternate hypothesis: at least one of the proportion differs from report proportions

Goodness of Fit Test

observed

expected

O - E

(O - E)² / E

155

186.400

-31.400

5.289

450

408.800

41.200

4.152

20

24.000

-4.000

0.667

160

164.800

-4.800

0.140

15

16.000

-1.000

0.063

Total

800

800.000

0.000

10.311

10.311

chi-square

4

df

.0355

p-value

Calculated chi square =10.311

Table value with 4 Df at 0.05 level =9.488

Calculated chi square =10.311 > 9.488 table value

The null hypothesis is rejected.

There is sufficient evidence to conclude that at least one of the proportion differs from report which stated proportions.