Problem 2: A coin was flipped 60 times and came up heads 36 times. (a) At the .1

Question

Problem 2:
A coin was flipped 60 times and came up heads 36 times.
(a) At the .10 level of significance, is the coin biased toward heads? Show your decision rule and calculations.

(b) Calculate a p-value and interpret it.

Problem 3:
The Web-based company Oh Baby! Gifts has a goal of processing 95 percent of its orders on the same day they are received. If 408 out of the next 500 orders are processed on the same day, would this prove that they are exceeding their goal, using a = .025? (See story.news.yahoo.com accessed June 25, 2004.)

Explanation / Answer

(2) Given n=60 , p=36/60 =0.6

(a)The test hypothesis is

H0: p=0.5
Ha: p>0.5

By using the normal approximation. The test statistic:

z=(0.6-0.5)/sqrt(0.5*0.5/60) = 1.55

Given =0.1, the critical value is Z(0.1)=1.282 (check normal table)

Since z=1.55>1.282, we reject Ho. SO the coin is biased.

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(b) The p-value is 0.0605

Since p-value is less than a=0.1, we reject Ho.

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(3) Given n=500, p =408/500=0.816

The test hypothesis is

Ho:p<=0.95

Ha:p>0.95

The test statistic is

z=(0.816-0.95)/sqrt(0.95*0.5/500) = -4.34

Given =0.025, the critical value is Z(0.025)=-1.96 (check normal table)

Since z=-1.96>-4.34, we do not reject Ho. SO we can not conclude that they are exceeding their goal.

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