QUESTIONS:

1. Suppose that a national survey finds that 73 percent of restaurant employees say that work stress has a negative impact on their personal lives. A random sample of 200 employees of a large restaurant chain finds that 141 employees say that work stress has a negative impact on their personal lives.

a. Can we perform a hypothesis test for this problem? Explain.

b. Formulate the null and alternative hypotheses needed to attempt to provide evidence that the percentage of work-stressed employees for the restaurant chain differs from the national percentage.

c. Use critical values and/or thep-value rule to perform the hypothesis test by setting the level of statistical significanceequal to 0.10 and 0.05. Interpret the results of the statistical test.

1. Air traffic controllers have the crucial task of ensuring that aircrafts don't collide. To do this, they must quickly discern when two planes are about to enter the same air space at the same time. They are aided by video display panels that track the aircraft in their sector and alert the controller when two flight paths are about to converge. The display panel currently in use has a mean alert time-which is the time that elapses between the instant when two aircrafts enter a collision course and when a controller initiates a call to reroute the planes-of 15 seconds. The alert times among all the aircrafts that are being used by an aircraft company is deemed to be normally distributed. A new display panel has been developed that uses artificial intelligence to project a plane's current flight path into the future. This new panel provides air traffic controllers with an earlier warning that acollision is likely. It is hoped that the mean alert timefor the new panel is less than 8 seconds. In order to test the new panel, 10 randomly selected air traffic controllers are trained to use the panel and their alert times for a simulated collision course are recorded. The sample alert times (in seconds) are: 7.2, 7.5, 8.0, 6.8, 7.2, 8.4, 5.3, 7.3, 7.6, 7.1.

a. What statistical test do we use in performing a hypothesis test for the population mean alert times in this case? Do we have sufficient information in order for us to perform hypothesis testing about the population means? Explain.

b. Test the null hypothesis versus the alternative hypothesis by settingequal to 0.05 and using a critical value.

c. Assuming that the sample size is not changed, what must be the highest possible value of so that we could not reject the null hypothesis at this level.