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Testing of proportion

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The lives of many people are affected by a fear that prevents them from flying. An institute for public opinion conducted a poll of 1014 adults, 48%of whom were men. The results reported in USAToday showed 12 % of the men and 33% of the women fear flying.

1. Construct a 95% confidence interval estimate of the difference between the percentage of men and the percentage of women who fear flying. Do the confidence interval limits contain 0, and what is the significance of whether they do or do not?

2. In a separate Gallup poll , 1001 randomly selected adults were asked this questions: "If you had to fly on an airplane tomorrow, how would you describe your feelings about flying? Would you-be very afraid, somewhat afraid, not very afraid, or not afraid at all? "Here are the responses: very afraid (18%) somewhat afraid (26%), not very afraid, (17%), not afraid at all (38%) and no opinion (1%). Are these Gallup poll results consistent with those obtained by the survey conducted by the Marist Institute for The Public Opinion? Explain. Can discrepancies be explained by the fact that the Gallup survey was conducted after the terrorist attacks of September 11,2001,whereas the other survey conducted before the date?

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Solution Summary

Testing of proportion based on Z test.

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Statistics: Union membership, Free school lunches, Automobile parts production

1. Union Membership Nationwide 13.7% of employed wage and salary workers are union members (down from 20.1% in 1983). A random sample of 300 local wage and salary workers showed that 50 belonged to a union. At ?=0.05, is there sufficient evidence to conclude that the proportion of union membership differs from 13.7%?

2. Free School Lunches It has been reported that 59.3% of U.S. school lunches served are free and at a reduced price. A random sample of 300 children in a large metropolitan area indicated that 156 of them received lunch free or at a reduced price. At the 0.01 level of significance, is there sufficient evidence to conclude that the proportion is less then 59.3%?

3. Automobile Part Production In an effort to increase production of an automobile part, the factory manager decides to play music in the manufacturing area. Eight workers are selected, and the number of items each produced for a specific day is recorded. After on week of music, the same workers are monitored again. The data are given in the table. At ?=0.05 can the manager conclude that the music has increased production?

Worker 1 2 3 4 5 6 7 8
Before 6 8 10 9 5 12 9 7
After 10 12 9 12 8 13 8 10

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