Question

Roy ‘s Texaco wants to keep the price of its unleaded gasoline competitive with that of other stations in the area. Roy’s is currently charging $1.29 per gallon. To check that the average price for this gasoline for all stations within a 15 mile radius is higher than his price, Roy randomly samples the price of unleaded gasoline at ten stations located in this area. He obtains the following data for the price per gallon (in dollars):

1.7, 1.5, 2.6, 2.2, 2.4, 2.3, 2.6, 3.0, 1.4, 2.3

Set up the appropriate hypotheses and test them using a significance level of α= .05

(2) How well do Airline companies serve their customers?. A study showed the following customer ratings: 3% excellent, 28% good, 45% fair, and 24% poor ( Business week, September 11, 2019). IN a follow up study of service by telephone companies, assume that a sample of 400 adults found the following customer ratings: 24 excellent, 124 good, 172 fair, and 80 poor. Is the distribution of the customer ratings for telephone companies different from the distribution of customer ratings for the Airline companies?. Set up the hypotheses to be tested and test with α=.01. what is your conclusion?.

Answer 1

( 1 )

For the given data

mean = 2.2

standard deviation = 0.5164

n = 10

(1) Null and Alternative Hypotheses

(5) Conclusion

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the the average price for this gasoline for all stations within a 15 mile radius is higher than his price, at the 0.05 significance level.

( 2 )

The following table is obtained:

Categories	Observed	Expected	(fo-fe)2/fe
Category 1	24	400*0.03=12	(24-12)2/12 = 12
Category 2	124	400*0.28=112	(124-112)2/112 = 1.286
Category 3	172	400*0.45=180	(172-180)2/180 = 0.356
Category 4	80	400*0.24=96	(80-96)2/96 = 2.667
Sum =	400	400	16.308

(5) Conclusion

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the distribution of the customer ratings for telephone companies different from the distribution of customer ratings for the Airline companies α=0.01 significance level.