calculating the probability for population proportion

Roper ASW conducted a survey to learn about American adults' attitudes toward money and happiness. 56% of the respondents said they balance their checkbook at least once a month.

a. Suppose a sample of 400 American adults were taken. Show the sampling distribution of the proportion of adults who balance their checkbook at least once a month .
b. What is the probability that the sample proportion will be within ± .02 of the population proportion?
c. What is the probability that the sample proportion will be within ± .04 of the population proportion?

Solution Preview

a. By the central limit theorem, the sampling distribution of proportion is normal with mean 0.56 and variance=56%*(1-56%)/400=0.000616

b. The lower limit of the sample proportion which is less than or equal to 0.02 from the population proportion = 0.56-0.02 = 0.54
The upper limit ...

Solution Summary

The solution gives detailed steps on calculating the probability for population proportion under different conditions.

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Calculating the Probability in Random Samples. ... to use Poisson distribution to calculate probabilities concerning the ... b. What is the probability that during a 1 ...

... 0.8665. The solution gives detailed steps on calculating probability for population proportion. All the formula and calcuations are shown and explained. ...

... Answer: 0.4314 or 43.14%. Calculates probability for sample proportions. ... Mean of the sampling distribution of proportion is the population proportion p= 48.00 ...

... Intermediate Calculations Z Value -1.959963985 Calculated Sample Size 800.303921. ... 1. Normal Probabilities. ...Probability for X > X Value 16.08 Z Value 1.33333333 P( ...

Statistics - Hypothesis Test on Population proportion. ... the probability that the sample proportion is 0.7 or more = 0.4562 Since calculated z value = - 0.11 ...

... appropriate formula that would be used to calculate the test ... c. The test statistic was calculated to be -2.02 ... with -2.02 is 0.0217 I used a calculator here: http ...