Question

A) To determine if chocolate milk was as effective as other carbohydrate replacement drinks, nine male cyclists performed an intense workout followed by a drink and a rest period. At the end of the rest period, each cyclist performed an endurance trial where he exercised until exhausted and time to exhaustion was measured. Each cyclist completed the entire regimen on two different days. On one day the drink provided was chocolate milk and on the other day the drink provided was a carbohydrate replacement drink.

Data consistent with summary quantities appear in the table below. (Use a statistical computer package to calculate the P-value. Subtract the carbohydrate replacement times from the chocolate milk times. Round your test statistic to two decimal places, your df down to the nearest whole number, and the P-value to three decimal places.)

Cyclist	Time to Exhaustion (minutes)
	1	2	3	4	5	6	7	8	9
Chocolate Milk	41.42	28.00	22.78	49.76	59.28	28.10	45.57	45.04	41.97
Carbohydrate Replacement	30.63	9.40	13.58	13.10	19.94	48.14	46.49	7.28	24.33

t	=
df	=
P	=

B) Some commercial airplanes recirculate approximately 50% of the cabin air in order to increase fuel efficiency. The researchers studied 1096 airline passengers, among which some traveled on airplanes that recirculated air and others traveled on planes that did not recirculate air. Of the 515 passengers who flew on planes that did not recirculate air, 104 reported post-flight respiratory symptoms, while 113 of the 581 passengers on planes that did recirculate air reported such symptoms. Is there sufficient evidence to conclude that the proportion of passengers with post-flight respiratory symptoms differs for planes that do and do not recirculate air? Test the appropriate hypotheses using α = 0.05. You may assume that it is reasonable to regard these two samples as being independently selected and as representative of the two populations of interest. (Use a statistical computer package to calculate the P-value. Use p_{do not recirculate} − p_{do recirculate}. Round your test statistic to two decimal places and your P-value to four decimal places.)

z	=
P	=

Answer 1

A) We use Paired t-test

= mean time to exhaustion for chocolate milk drink.

= mean time to exhaustion for Carbohydrate replacement drink.

and

= carbohydrate replacement times from the chocolate milk times.

=   - = Difference in mean exhaustion time of cyclist player between the day provided Chocolate milk drink and Carbohydrate replacement drink.

Hypothesis:

Ho: = 0

Ha: > 0

Computational Table:

D = Chocolate milk - Carbohydrate replacement.

	Chocolate milk	Carbohydrate Replacement	D	D2
	41.42	30.63	10.79	116.4241
	28	9.4	18.6	345.96
	22.78	13.58	9.2	84.64
	49.76	13.1	36.66	1343.956
	59.28	19.94	39.34	1547.636
	28.1	48.14	-20.04	401.6016
	45.57	46.49	-0.92	0.8464
	45.04	7.28	37.76	1425.818
	41.97	24.33	17.64	311.1696
Total	361.92	212.89	149.03	5578.05

Calculation:

Test statistic:

Degrees of Freedom: n-1 = 9-1 = 8

P-value: 0.018  

Conclusion:

P-value < , 0.018 < 0.05, That is Reject Ho at 5% level of significance.

Therefore, chocolate milk was as effective as other carbohydrate replacement drinks.