You are the manager of a fast-food restaurant. The business...

You are the manager of a fast-food restaurant. The business problem is to determine whether the population mean waiting time to place an order has changed in the past month from its previous population mean value of 4.5 minutes. From past experience, you can assume that the population is normally distributed, with a population standard deviation of 1.2 minutes. You select a sample of 25 orders during a one-hour period. The sample mean is 5.1 minutes. Use the level of significance ? = 0.05 to determine whether there is evidence that the population mean waiting time to place an order has changed in the past month from its previous population mean value of 4.5 minutes. Write the null and alternative hpotheses and make the decision using two different approaches: (a) The critical value approach. (b) The p -value approach.

Transcript

00:01 So a question says that you are the manager of a fast food restaurant and the business problem is to determine whether the population mean waiting time to place an order has changed in the past few months from its previous population mean value of 4 .5 minutes.

00:14 From past experience, you can assume that the population is normally distributed with a population standard division of 1 .2 minute.

00:22 You select a sample of 25 orders during a 1 hour period.

00:26 The sample mean is 5 .1 minute.

00:28 Use the level of significance of alpha is equals to 0 .05 to determine whether there is evidence that the population mean the population mean waiting time to place an order has changed in the past month from its previous population mean value of 4 .5 minutes we're supposed to write the null and alternative hypothesis and make the decision using two approaches both the critical value approach and the pay value approach so let's go into our worksheet and extract out all of the necessary details so our population mean meal is actually cost to 4 .5 minutes our samples ice and is across to 2 .5 excuse me our sample size end is across to 25 rather our population standard deviation sigma we have that to be equals to 1 .2 our sample in x -bar we have that to be equals to 5 .1 and our alpha level is going to be 0 .05 so the first step is to state the null and alternative hypothesis and then we have that to be that h not is based on the fact that mu is equal to 4 5 and the alternative hypothesis is that m is not equals to 4 .5 since you are trying to test that there has been a change so the change can either be a decrease in the waiting time or an increase in the waiting time so since the direction of change was not instigated was not mentioned it simply implies that our test is a non -directional test which you can also call it to till test so the next step is for us to get the test statistics of our results result and then to do so we have to take a closer look at our details given to us in our question we have the value of the population mean we have the value of the population of the standard division these details alone are enough for us to know that our data sets is normally distributed so that means our test statistics is going to be a z test so we have that z is equal to xx minus mu divided by zima divided by the square root of n x by in this case is 5 .1 minus our meal is 4 .5 divided by our sigma is actually 1 .2 divided by the square root of 205...

Question

Please give Ace some feedback