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?

Comprehend the process of theory development as utilized in Roy's Adaptation Model.

Grasp the underlying assumptions adapted to Roy's Model for the 21st Century.

Recognize the application of Roy's Adaptation Model in understanding coping mechanisms.

Illustrate the significance of environmental stimuli in the adaptation process.

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Definitions:

Standard Deviation

A measure of the amount of variation or dispersion of a set of values, indicating how much the values diverge from the mean.

Correlation

A statistical measure that describes the extent to which two variables change together, indicating a relationship but not causality.

Dividend Yield

A financial ratio indicating how much a company pays out in dividends each year relative to its stock price.

Total Return

The overall financial gain or loss on an investment over a specified time period, including both capital gains and interest or dividends.