Perform the Indicated Goodness-Of-Fit Test Using the P-Value Method At the 5% Significance Level, Do the Data Provide Evidence

Essay

Perform the indicated goodness-of-fit test using the P-value method. Be sure to state the hypotheses and the significancelevel , to compute the value of the test statistic, to obtain the P-value, and to state your conclusion.
-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. $\begin{array}{l} \begin{array} { c c } \frac { \text { Months } } { \text { Under 60 } } & \text { Relative Frequency } \\ 70 - 79 & 0.017 \\ 80 - 89 & 0.201 \\ 90 - 99 & 0.353 \\ 100 - 109 & 0.331 \\ & 0.098 \end{array}\\ \text { A random sample of } 448 \text { engines from the firm's Ohio plant gives the following results. }\\ \begin{array} { l r } \frac { \text { Months } } { \text { Under } 60 } & \text { Number of engine } \\ 70 - 79 & 22 \\ 80 - 89 & 131 \\ 90 - 99 & 46 \\ 100 - 109 & 154 \\ \hline \end{array} \end{array}$ 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?