Managers who engage in “coopetition.” In business, firms that both cooperate and compete with other firms are described as engaging in “coopetition.” A study published in Industrial Marketing Management (February 2016) examined the level of external tension experienced by managers who engage in coopetition. External tension (measured on a 20-point scale) was recorded for each in a sample of 1,532 managers, all from firms that were engaged in coopetition. The sample mean tension was x=10.82 and the sample standard deviation was s=3.04.

Conduct a test (using a=.05) to determine if the true mean external tension level of all managers who engage in coopetition differs from 10.5 points.

Random sample\((n)\,\,\, = 1532\)

Sample mean\((\bar x)\,\,\, = \,\,10.82\)

Standard deviation\(\sigma \,\, = \,3.04\)

Null and alternative hypothesis are as follows

\(\begin{aligned}{l}H0:\,\mu \,\, = \,10.5\\H\alpha :\,\mu \,\, \ne 10.5\end{aligned}\)

Using the central tendency, variation, sample size, and several predictor variables in your statistical model, the test statistic sums up the observed data into a single number.

The data distribution, which can be described by its central tendency and variation around that central tendency, determines the frequency with which each observation occurs.

Because different statistical tests predict distribution types, selecting the appropriate statistical test for your hypothesis is critical.

The formula for test statistics is as follows.

\(\begin{aligned}{l}z &= \frac{{\bar x - \mu }}{{\sigma /\sqrt n }}\\z &= \frac{{10.82 - 10.5}}{{3.04/\sqrt {1532} }}\\z &= \frac{{0.32}}{{3.04/39.14}}\\z &= \frac{{0.32}}{{0.0776}}\\z &= \,\,4.12\end{aligned}\)

The critical value is as follows.

\(\begin{aligned}{l}z\alpha /2 = \,\,z0.05\\z\alpha /2 = \,\,1.645\end{aligned}\)

So \(z > zcritical\), reject the null hypothesis. There is sufficient proof to conclude that the actual mean exterior tension level of managers interacting in encroachment differs from 10.5 points.