342Exam

9.54
Faced with rising telefax costs, a firm issued a guideline that transmissions of 10 pages or more
should be sent by 2-day mail instead. Exceptions atomic number 18 allowed, but they want the average to be 10
or below. The firm examined 35 randomly chosen fax transmissions during the next year, yielding
a sample mean of 14.44 with a precedent deviation of 4.45 pages. (a) At the .01 level of significance,
is the true mean great than 10? (b) Use Excel to find the right-tail p-value.

(a)
H0: mu = 10
H1: mu > 10

one-tail t-test with a = 0.01; vital value for 34 df = 2.326
Test statistic:

T = (14.44-10)/[4.45/sqrt(35)] = 5.9028

Since T > 2.326 weject H0 and decide that there is statistical evidence that the true mean is > 10

(b) p-value = 0.00000057579

9.56
A coin was flipped 60 times and came up heads 38 times. (a) At the .10 level of significance, is the
coin biased toward heads? Show your decision ordinance and calculations. (b) Calculate a p-value and
interpret it.
(a)

phat = 38/60 = 0.6333

H0: p = 0.5
H1: p > 0.5

a = 0.10

Test statistic Z = (phat - p)/sqrt[p(1-p)/n] = (0.6333 - 0.5)/sqrt[0.5(1-0.5)/60] = 2.065

Decision normal: Reject H0 if Z > 1.2816

Since 2.065 > 1.2816 we extinguish H0 and shut down that the coin is biased.

(b)
p-value = 0.



019434
Since the p-value < 0.10 we reject the null hypothesis and conclude that the coin is biased.
9.62
The Web-based company Oh flub! Gifts has a goal of processing 95 percent of its orders on the
same day they are received. If 485 out of the next vitamin D orders are processed on the same day, would
this prove that they are exceeding their goal, using ? = .025? (See story.news.yahoo.com) access
H0: p = 0.95
H1: p > 0.95
Decision command: Reject H0 if z > 1.96.
Test statistic Z = (phat-p)/sqrt[p*(1-p)/n] = (485/500-0.95)/sqrt(0.95*(1-0.95)/500) = 2.0519
Since 2.01519 > 1.96 we reject H0 and conclude that they are exceeding their goal.

9.64
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