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Chapter 9: Q.108 (page 555)

A recent survey in the N.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 that 142 owned some type of stock. At the 0.05 significance level, can the survey be considered to be accurate?

Short Answer

Expert verified

The survey does not appear to be accurate.

Step by step solution

01

State the null and alternate hypothesis. we have to conduct hypothesis test if families of N.Y take 48.8% of families own stock or not, on average. 

H0:p=0.488;Ha:p≠0.488

02

Calculate the p-value using the normal distribution for proportions: 

p-value=0.0114

In one to two complete sentences, explain what the p-value means for this problem. If the null hypothesis is true (the proportion is 0.488), then there is a 0.0114 probability that the sample (estimated) proportion is 0.568 or more.

03

Compare α and the p-value:Indicate the correct decision (“reject” or “do not reject” the null hypothesis), the reason for it, and write an appropriate conclusion, using complete sentences.

alphadecisionreason for decision
0.05Do not reject the null hypothesis.
p-value>0.05

Conclusion: At the 5% level of significance, there is enough evidence to conclude that 48.8% of families own stocks.

04

accuracy of the survey

The survey does not appear to be accurate.

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Most popular questions from this chapter

A statistics instructor believes that fewer than 20% of Evergreen Valley College (EVC) students attended the opening midnight showing of the latest Harry Potter movie. She surveys 84 of her students and finds that 11 of them attended the midnight showing. The Type I error is to conclude that the percent of EVC students who attended is ________.

a. at least 20%, when in fact, it is less than 20%.

b. 20%, when in fact, it is 20%.

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d. There is not enough evidence to conclude that the mean number of hours is more than 4.75

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