A new bus route has been established between downtown Chicago and Springfield. Dan has taken the bus to work for many years. For the old bus route, he knows from long experience that the mean waiting time between buses at his stop was u = 20 minutes. However, a random sample of 5 waiting times between buses using the new route had a mean x= 15.1 minutes with sample standard deviation s = 6.2 minutes. Does this indicate that the population mean waiting time for the new route is shorter than what it used to be? Use a= 0.05. Assume that x is normally distributed.
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1. What is the level of significance? State the null and alternate hypotheses. Will you use a left tailed, right tailed or two tailed test?
2. Identify the sampling distribution you will use: the standard normal or Student's t distribution. What is the value of the sample test statistic?
3. Find (or estimate) the P value. Sektch the sampling distribution and show the area corresponding to the P value. (alternate method: Find the critical value(s) and sketch the critical regions and sample test statistic on the normal curve).
4. Based on your answers, will you reject or fail to reject the null hypothesis?
5. Interpret your decision in the context of the application.