An urn contains 6 red marbles and 3 white ones. Two marbles are selected at random from the urn, their colors are noted, and then the marbles are replaced in the urn. This process is performed a total...

An urn contains 6 red marbles and 3 white ones. Two marbles are selected at random from the urn, their colors are noted, and then the marbles are replaced in the urn. This process is performed a total of 120 times, and the results obtained are shown in Table 12.21.

(a) Determine the expected frequencies.

(b) Determine at a significance level of 0.05 whether the results obtained are consistent with those expected.

1. Two hundred bolts were selected at random from the production of each of four machines. The numbers of defective bolts found were 2, 9, 10, and 3. Determine whether there is a significant difference between the machines, using a significance level of 0.05.