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Chapter 8: Q.45 (page 497)

Election polling Gloria Chavez and Ronald Flynn are the candidates for mayor in a large city. We want to estimate the proportion pof all registered voters in the city who plan to vote for Chavez with 95% con铿乨ence and a margin of error no greater than 0.03. How large a random sample do we need? Show your work.

Short Answer

Expert verified

From the given information, the sample size of the registered voter is1068

Step by step solution

01

Given Information

It is given in the question, the margin of errorE=0.03

confidence interval95%

How large a random sample do we need?

02

Explanation

Confidence interval is 95%

Convert 95%into decimal.

95100=0.95

For confidence interval 0.95,use table A.

z伪/2=1.96

Since the sample proportion p鈭�is unknown.

Calculate sample size. Use the formula n=[z伪/2]2脳0.25E2

n=[z伪/2]2脳0.25E2

n=1.962脳0.250.032

=1068

Hence, the required sample size is1068.

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Most popular questions from this chapter

In each of the following settings, check whether the conditions for calculating a confidence interval for the population proportion p are met.

1. An AP Statistics class at a large high school conducts a survey. They ask the first 100 students to arrive at school one morning whether or not they slept at least 8 hours the night before. Only 17 students say "Yes."

2. A quality control inspector takes a random sample of 25 bags of potato chips from the thousands of bags filled in an hour. Of the bags selected, 3 had too much salt.

To assess the accuracy of a laboratory scale, a standard weight known to weigh 10grams is weighed repeatedly. The scale readings are Normally distributed with unknown mean (this mean is 10grams if the scale has no bias). In previous studies, the standard deviation of the scale readings has been about 0.0002gram. How many measurements must be averaged to get a margin of error of 0.0001with 98% confidence? Show your work.

What inference method will you use? Check that the conditions for using this procedure are met.

Many teens have posted profiles on sites such as Facebook and My Space. A sample survey asked random samples of teens with online profiles if they included false information in their profiles. Of 170younger teens (ages 12to 14) polled, 117said 鈥淵es.鈥� Of 317older teens (ages 15to 17) polled, 152 said 鈥淵es.鈥�6 A 95% confidence interval for the difference in the population proportions (younger teens 鈥� older teens) is 0.120 to 0.297. Interpret the confidence interval and the confidence level

You have measured the systolic blood pressure of an SRS of 25company employees. A 95%confidence interval for the mean systolic blood pressure for the employees of this company is (122,138). Which of the following statements gives a valid interpretation of this interval?

(a) 95%of the sample employees have systolic blood pressure between 122and138.

(b) 95%of the population of employees have systolic blood pressure between 122and138.

(c) If the procedure were repeated many times, 95%of the resulting confidence intervals would contain the population mean systolic blood pressure.

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(e) If the procedure were repeated many times, 95%of the sample means would be between122and138.
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