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Chapter 9: Q. 108 (page 555)

A recent survey in theN.Y. Times Almanac indicated that 48.8%of families own stock. A broker wanted to determine if this survey could be valid. He surveyed a random sample of 250 families and found that142owned some type of stock. At the 0.05 significance level, can the survey be considered to be accurate?

Short Answer

Expert verified

There is insufficient evidence to conclude that48.8%of families own stock.

Step by step solution

01

Given information

x=142,n=250,p0=0.488,a=0.05

02

Explanation

State the hypothesis:

The null hypothesis states that 48.8%of families own stock. In symbols:

H0:p=0.488

The alternative hypothesis states that not 48.8%of families own stock. In symbols:

Ha:p≠0.488

The sample proportion is:

p⏜=xn=142250=0.568

The test statistic is:

z=p⏜-p0p01-p0n=0.568-0.4880.4881-0.488250=0.0800.0316=2.53

The p-value is:

p-value=Pz<-2.53+Pz>2.53=0.0057+0.0057=0.0114

Since the null hypothesis is rejected, there is insufficient evidence to conclude that 48.8%of families own stock.

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