Question: A firm that manufactures engines for racing boats gathers data from all of its plants. The table below gives the distribution of the life span of the engines (in numbers of months) for the entire firm.

Months Relative Frequency

Under 60 0.017

70-79 0.201

80-89 0.353

90-99 0.331

100-109 0.098

A random sample of 448 engines from the firm's Ohio plant gives the following results.

Months Number of engines

Under 60 22

70-79 131

80-89 46

90-99 154

100-109 95

At the 5% significance level, do the data provide evidence that the distribution of the life spans of the engines manufactured at the Ohio plant is different from the firm's overall distribution?

a) What is the p-value for this test?

b) What is your decision (Reject/Fail to reject)?