A suburban bus company is considering the institution of a commuter bus route fr

Question

A suburban bus company is considering the institution of a commuter bus route from a particular suburb into the central business district of the city. The company has determined that the route will be profitable if more than 25% of the commuters ride the route. A) The company has no prior information regarding the proportion of commuters who would use this bus route. They are interested in calculation a 99% confidence interval estimate of the proportion who would use the bus route, with a maximum error of .05. What is the required sample size? B) Suppose the company had a pilot sample. Explain how this information would affect the required sample size as compared to your answer in part a. Specifically, under what conditions would it increase, decrease, or remain unchanged? Explain C) A random sample of 300 commuters from the relatively large suburb is selected. Suppose that 70 of the selected commuters indicate that they would use the bus route. Calculate a 99% confidence interval for the proportion of all commuters in this suburb who would utilize this potential bus route. D) Suppose that the company conducts a sample of 300 customers and that 90 of the sampled individuals indicate that they would use the route. Is there sufficient evidence to indicate that the new route would be profitable, at a 5% level of significance? State the null and alternative hypothesis. E) Calculate the p value for your test of part c. Interpret

Explanation / Answer

Excel formula:

A) Sample size calculation given p= 0.25 ERROR E= 0.05 z (for 99%CI)= 2.575829 So, Sd= 0.433013 sample size n= (z*Sd/E)^2 497.6172 So at least 498 must be surveyed b) If sample size is less than 498, error will increase. For less error, we should have more samples. c) given p= 0.233333 z (for 99%CI)= 2.575829 So, SE= 0.024419 CI: Upper= 0.296233 lower= 0.170434 d) we nned to do z proportion hypothesis testiing H0: p<=.25 Ha: p>.25 (right tailed z test) given p= 0.3 Point estimate= 0.05 So, SE= 0.025 z-score= 2 p-value= 0.02275 p-value<0.05 then reject H0; yes p>.25 so go ahead & start service

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