4 16 Pts An Article In The Des Moines Register On Sunday October 23 2005 Reported On A Survey Of 1 001 Randomly Sel 1 (79.04 KiB) Viewed 32 times
4. [16 pts] An article in the Des Moines Register on Sunday, October 23, 2005 reported on a survey of 1,001 randomly selected adults in the U.S. that was taken August 22-24, 2005. In the survey, the adults were asked; "Compared to 20 or 30 years ago do you think people are more rude, less rude or about the same.” 69% of the survey respondents answered "more rude." a) [2] What is the population? b) [2] What is the sample? c) [5] Are the conditions for constructing a confidence interval for the population proportion satisfied? Support your answer. d) [5] Construct a 98% confidence interval on the population proportion of all adults who would answer the question "more rude." e) [2] Will a 90% confidence interval be wider of narrower than the one you constructed in d)? You do not need to construct a new interval to answer this question
(16 pts] A manufacturer is concerned because during the final inspection of items it currently rejects, and therefore cannot sell, 12% of its product. A new process is introduced that hopefully will reduce the proportion of rejected items. After the new process has been in place for a while, a random sample of 100 parts is selected and inspected. Of those 100 items 8 are rejected. We want to know if the new process has been effective in reducing the proportion of rejected parts? a) [3] Set up the appropriate null and alternative hypotheses. Be sure to clearly define what the population proportion is. b) [3] Are the conditions for statistical inference met? Explain briefly. c) [4] Compute the value of the test statistic and the associated P-value. d) [2] Use the P-value to make a decision. e) [4] State your conclusion within the context of the problem.
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