In politics, marketing, etc. we often want to estimate a percentage or proportion p. One calculation in statistical polling is the margin of error - the largest (reasonble) error that the poll could have. For example, a poll result of 72% with a margin of error of 4% indicates that p is most likely to be between 68% and 76% (72% minus 4% to 72% plus 4%). In a (made-up) poll, the proportion of people who like dark chocolate more than milk chocolate was 33% with a margin of error of 1.9%. Describe the conclusion about p using an absolute value inequality.

A programmer plans to develop a new software system. In planning for the operating system that he will​ use, he needs to estimate the percentage of computers that use a new operating system. How many computers must be surveyed in order to be 95​% confident that his estimate is in error by no more than four percentage points? Complete parts​ (a) through​ (c) below.

A company wants to determine the frequency of the occurrence of invoice errors. Suppose that in a sample of 100 sales invoices, 10 contain errors. construct a 90% CI for the proportion error.

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A programmer plans to develop a new software system. In planning for the operating system that he will​ use, he needs to estimate the percentage of computers that use a new operating system. How many computers must be surveyed in order to be 95​% confident that his estimate is in error by no more than two percentage points? Complete parts​ (a) through​ (c) below.

The table to the right is based on the assumption that 1% of breast tumors are malignant. It also assumes that mammogram screening is 90% accurate. Complete parts (a) through (c) below. Positive Mammogram Negative Mammogram Total % (Type an integer or decimal rounded to the nearest tenth as needed.) b. What is the chance of a positive mammogram, given that the patient has cancer? % (Type an integer or decimal rounded to the nearest hundredth as needed.) Tumor is Tumor is Malignant Benign 90 1206 a. Suppose a patient has a positive mammogram. What is the chance that she really has cancer? 10 100 8694 9900 % (Type an integer or decimal rounded to the nearest tenth as needed.) c. Suppose a patient has a negative mammogram. What is the chance that she actually does have cancer? Total 1296 8704 10,000

Polls. America OnLine published a survey question. Among the 2,300 Internet users who responded, 20% answered “yes” and the others answered “no.” For the “yes” responses, what is the value of pn? What is fundamen-tally wrong with this survey?

In politics, marketing, etc. we often want to estimate a percentage or proportion p. One calculation in statistical polling is the margin of error - the largest (reasonble) error that the poll could have. For example, a poll result of 72% with a margin of error of 4% indicates that p is most likely to be between 68% and 76% (72% minus 4% to 72% plus 4%).   In a (made-up) poll, the proportion of people who like dark chocolate more than milk chocolate was 37% with a margin of error of 2.5%. Describe the conclusion about p using an absolute value inequality.   . That lets you type in a vertical bar | to represent absolute values. Also, when you type in  <  and then =, the symbolic entry option will automatically convert that to  ≤ . In the same way, if you type in  >  and then =, the symbolic entry option will automatically convert that to  ≥.   Be sure to use decimal numbers in your answer (such as using 0.40 for 40%).

Medical Marijuana? An international poll of physicians was conducted on the New England Journal of Medicine website asking “Do you believe that the overall medicinal benefits of marijuana outweigh the risks and potential harms?” Identify the a. specified attribute. b. population. c. population proportion. d. Of the 1446 physicians who responded, 76% said yes. Is the proportion 0.76 (76%) a sample proportion or a population proportion? Explain your answer.

We'd like to know the percentage of people living in California who owns a cell phone. How many people in California must be surveyed in order to be 95% confident that the sample proportion is in error by no more than 4 percentage points?