1. Does one national airline consistently leave the departure gate later than the another, or not? To determine this, random samples of 15 flights from each airline were taken on a randomly chosen weekday during the summer months (when there are no weather issues). The difference in minutes between the time the flight is to pull-away from the gate and the actual time the flight pulled away from the gate is the variable being measured, a variable called the "delay". Positive values indicate the flight was late in pulling away from the gate (negative values indicate the flight left the gate earlier than scheduled). The data is given here. Use alpha = 0.05 for all calculations below Airline A: 3.7, 3.1, 5.6, 8.1, 4, 4, 2.8, 6.2, 4, 9.5, 3.1, 7, 2.8, 3.8, 2.4; Airline B: 11.4, 19.6, 2.8, 7.1, 10.5, 1.7, 14, 4, 13.7, 12.2, -3.6, 3, 9.1, 3.2, 16.5;

You wish to conduct a statistical test to see if there is a difference between Airlines A and B in the variable "delay". (a) Does this data indicate that the variable of interest is normally distributed? Use available technology to create the most appropriate graph or graphs. Select the statement that is closest to your findings. A. The data suggests that delay is normally distributed for Airline A and normally distributed for Airline B. B. The data suggests that the variability in the delay is less for Airline A than Airline B. C. The data suggests that the variability in the delay is more for Airline A than Airline B. D. The data suggests that delay is not normally distributed for Airline A and normally distributed for Airline B. E. The data suggests that the variability in the delay is the same for Airline A and Airline B. F. The data suggests that delay is not normally distributed for Airline A and not normally distributed for Airline B. G. The data suggests that delay is normally distributed for Airline A and not normally distributed for Airline B. (b) Construct the most appropriate statistical hypotheses that will test if there is a difference between Airlines A and B. A. H0:A=BHA:AB. H0:A=BHA:A>B C. H0:~A=~BHA:~A~B D. H0:A=BHA:AB E. H0:~A=~BHA:~A>~B F. H0:~A=~BHA:~A<~B (c) Find the value of the test statistic for this test, use at least one decimal in your answer. Test Statistic =

(d) Determine the P-value of your statistical test in part (c), and report it to at least four decimal places. P=

(e) At =0.05, this data suggested that the null hypothesis should ? be rejected. not be rejected There is ? a significant difference not a significant difference between the delay in Airline A flights and Airline B flights.

2. A professor in the school of business at a certain university wants to investigate the claim that the prices of new textbooks in the campus store are higher than a competing national online bookstore. The professor randomly chooses required texts for 12 business school courses. The data is given in the table below.

Book	Campus Store	Online Store
A	208.19	206.74
B	92.75	93.67
C	194.54	190.96
D	168.39	164.48
E	90.63	87.3
F	222.45	221.45
G	193.38	194.27
H	246.05	245.66
I	144.11	143.13
J	160.54	163.07
K	143.99	143.13
L	161.87	160.69

(a) Let XA denote the price of books at the campus store, and XB be the price of books at the online store, also let XD=XAXB. Choose the correct statistical hypotheses. A. H0:D=0HA:D>0 B. H0:campus=online,HA:campusC. H0:D=0,HA:D0 D. H0:D=0,HA:D<0 E. H0:D=0,HA:D<0 F. H0:campus=online,HA:campusonline G. H0:D>0,HA:D<0 H. H0:campus=online,HA:campus>online (b) Carry out the appropriate statistical test and find the P-value, to at least three decimal places. P=

(c) Based on the above calculations, we should ? reject not reject the null hypothesis. Use =0.05. (d) Using the technology available to you, create the most appropriate graph(s) to check the assumption(s) that need to be satisfied for your inferences in (b) and (c) to be valid. What statement below aligns with your findings? A. The prices charged at the online bookstore are normally distributed. B. The differences in the price of a textbook at the campus bookstore and the price of the textbook at the online store are not normally distributed. C. The differences in the price of a textbook at the campus bookstore and the price of the textbook at the online store are normally distributed. D. The prices charged at the campus bookstore are not normally distributed. E. The prices charged at the campus bookstore are normally distributed. F. The prices charged at the online bookstore are not normally distributed.

4. Ten randomly selected people took an IQ test A, and next day they took a very similar IQ test B. Their scores are shown in the table below.

Person	A	B	C	D	E	F	G	H	I	J
Test A	81	116	72	100	110	106	100	129	96	90
Test B	80	113	71	105	112	104	104	130	94	93

Consider (Test A - Test B). Use a 0.01 significance level to test the claim that people do better on the second test than they do on the first. Assume differences are normal. (Note: You may wish to use software.)

(a) The test statistic is (at least 2 digits after the decimal)

(b) The critical value is (at least 3 digits after the decimal)

(c) Is there sufficient evidence to support the claim that people do better on the second test? A. Yes B. No

(d) Construct a 99% confidence interval for the mean of the differences. Again, use (Test A - Test B) Use 3 digits after the decimal. <<

3. Jonathan considers booking a flight to see the temple at Chichen Itza, which is near Cancun Mexico. Expedica.ca offers both business class (non-stop/direct) as well as first class flights (with a 1-stop layover). Jonathan wants to know if the prices for his options are approximately the same, or if flying first class will generally cost more. Can you help him find this out? Use =0.038 for all calculations. The specifics can be found in the file below.

	Non_Stop_Flights	one_Stop_flights
1	1779.45	1473.97
2	1579.93	1603.86
3	1373.3	1510.51
4	1361.2	2150.6
5	1767.15	1431.54
6	1579.18	2054.63
7	1631.3	1501.49
8	1535.21	1671.76
9		1478.77
10		1944.15

(a) Check to see if the distribution of the flight classes appear to be normal. Hint: use a probability plot to decide with =0.038. A.direct flights appear to be normal but layover flights do not appear to be normal B.neither direct flights nor layover flights appear to be normal C.Both direct flights and layover flights appear to be normal D.layover flights appear to be normal but direct flights do not appear to be normal (b) Report the p-value of the test you ran in (a) concerning the normality of first class flights, use at least two decimals in your answer. P-value =

(c) Does there appear to be a negative difference in the general price between business and first class flights? A.I don't have enough information to answer this question B.No C.I have too much information to answer this question D.Yes (d) At what level of significance would you come to a different conclusion? Please use at least four digits in your answer. Give a decimal not a percentage. Significance Level =

(e) Based on the above calculations, to save money Jonathan should ? buy a business class (direct) flight buy a first class (layover) flight buy a business class (layover) flight buy a first class (direct) flight buy either a first or business class flight, since the difference is negligible.