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

question 26

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?

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Definitions:

Specification Limits

Pre-determined upper and lower bounds within which a product or process's performance is considered acceptable.

Standard Deviations

An indicator of the degree of spread or variability in a collection of data points, showing how much the values differ from the average.

Sample Proportion

An estimate of the proportion within the entire population that possesses a particular attribute, derived from a subset of the population.

Manufacturing Process

The procedure through which raw materials are transformed into finished products through various mechanical, chemical, or physical operations.