Q45E Managers who engage in 鈥渃oopet... [FREE SOLUTION]

91影视

Statistics For Business And Economics

James T. McClave, P. George Benson, Terry Sincich

$Math Studyset 91影视 Explanations$ Math

13th Edition 路 888 pages

ISBN: 9780134506593

Chapter 7: Q45E (page 412)

Managers who engage in 鈥渃oopetition.鈥� In business, firms that both cooperate and compete with other firms are described as engaging in 鈥渃oopetition.鈥� 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.

Short Answer

Expert verified

$z = \,4.12$

Step by step solution

Given information

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

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

Standard deviation$\sigma \,\, = \,3.04$

Null and alternative hypothesis are as follows

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

Test Statistics

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.

Step 3:

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.