A manufacturing plant has preliminary contracts with three different suppliers of machines. Each supplier delivered 15 machines, which were used in the plant for four months in preliminary production. It turned out that one of the machines from supplier 1 was defective, seven of the machines from supplier 2 were defective, and seven of the machines from supplier 3 were defective. The plant statistician decided to test the null hypothesis H0 that the three suppliers provided the same quality. Therefore, he set up Table 10.28 and carried out a χ2 test. By summing the values in the bottom row of Table 10.28, he found that the value of the χ2 statistic was 24/5 with two degrees of freedom. Hethen found from a table of the χ2 distribution that H0 should be accepted when the level of significance is 0.05. Criticize this procedure and provide a meaningful analysis of the observed data.
Table 10.28 Data for Exercise 5

Supplier 80 3 Number of defectives N Expected number of defectives 7 7 5 E under Ho 16 4 4