Question

Each person in a random sample of 227 male teenagers and a random sample of 302 female teenagers was asked how many hours he or she spent online in a typical week. The sample mean and standard deviation were 15.1 hours and 11.2 hours for males and 14.3 and 11.7 for females. (Use a statistical computer package to calculate the P-value. Use μ_males − μ_females. Round your test statistic to two decimal places, your df down to the nearest whole number, and your P-value to three decimal places.)

t =
df =
P =

o 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	21.87	25.61	39.86	45.84	28.69	20.54	37.23	31.64	35.13
Carbohydrate Replacement	14.62	19.51	43.05	15.28	10.35	6.92	47.80	9.08	11.16

t	=
df	=
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Some commercial airplanes recirculate approximately 50% of the cabin air in order to increase fuel efficiency. The researchers studied 1104 airline passengers, among which some traveled on airplanes that recirculated air and others traveled on planes that did not recirculate air. Of the 519 passengers who flew on planes that did not recirculate air, 106 reported post-flight respiratory symptoms, while 112 of the 585 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.)

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Answer 1

1)

Unknown But Unequal Variances There ae situations where the analyst is not able to assume that q--σ2. Recall from Section 9.8 that, if the populations are normal, the statistic T 1-)-do has an approximate t-distribution with approximate degrees of freedom As a result, the test procedure is to not reject Ho when with v given as above. Again, as in the case of the pooled t-test, one-sided alter natives suggest one-sided critical regions.

Two-Sample T-Test and CI

Sample    N Mean StDev SE Mean
1       227 15.1   11.2     0.74
2       302 14.3   11.7     0.67

Difference = μ (1) - μ (2)
Estimate for difference: 0.80
95% CI for difference: (-1.17, 2.77)
T-Test of difference = 0 (vs ≠): T-Value = 0.80 P-Value = 0.425 DF = 497