# Confidence interval for mean and proportion

1. Find the critical value za/2 which corresponds to a degree of confidence of 98%.

2. Express the confidence interval in the form of p-hat plus or minus E.

-0.052 < p < 0.568

3. Find the margin of error for the 95% confidence interval used to estimate the population proportion if n = 175 and x = 95.

4. Find the minimum sample size you should use to assure that your estimate of p-hat will be within the required margin of error around the population p:

margin of error = 0.001, confidence level = 92%,

p-hat and q-hat are unknown.

5. The following confidence interval is obtained for a population proportion, p: (0.458, 0.490)

Use these confidence interval limits to find the point estimate, p-hat.

6. Use the confidence level and sample data to find a confidence interval for estimating the population mean .

Test Scores: n = 101, x-bar = 96.8, sigma = 8.3, 99 percent confidence

7. Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation sigma. Assume that the population has a normal distribution.

Weight of men: 90% confidence; n=14, x-bar = 155.7 lb; s = 13.6 lb.

8. A researcher wishes to construct a 95% confidence interval for a population mean. She selects a simple random sample of size n=20 from the population. The population is normally distributed and sigma is unknown. When constructing the confidence interval, the researcher should use the t distribution; however, she incorrectly uses the normal distribution. Will the true confidence level of the resulting confidence interval be greater than 95%, smaller than 95%, or exactly 95%?

9. Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p: n = 60, x = 19, 95 percent.

10. Use the confidence level and sample data to find the margin of error E.

Weights of eggs: 95% confidence; n = 49, x-bar = 1.70 oz, sigma = 0.33 oz

11. Find the critical value Chi squared R corresponding to a sample size of 3 and a confidence level of 95 percent.

Round to the nearest three decimal places.

12. Find the appropriate minimum sample size: You want to be 95% confident that the sample variance is within 40% of the population variance. Remember, sample size must be an integer.

13. The confidence interval: 5.06 < sigma2 < 23.33 is for the population variance based on the following sample statistics:

n = 25, x-bar = 41.2, and s = 3.1

What is the degree of confidence? Use only integers, no % sign and no decimal places.

14. Find the margin of error. 95% confidence interval; n = 91 ; x-bar = 55, s = 5.4

Round to the nearest two decimal places.

https://brainmass.com/statistics/confidence-interval/confidence-interval-for-mean-and-proportion-129642

#### Solution Summary

The solution gives the complete steps the construction of confidence interval for population mean and proportion.

Confidence Interval: Proportion of Drug Test

As a condition of employment, Fashion Industries applicants must pass a drug test. Of the last 220 applicants 14 failed the test. Develop a 99 percent confidence interval for the proportion of applicants that fail the test. Would it be reasonable to conclude that more than 10% of the applicants are now failing the test? In addition to the testing of applicants, Fashion Ind. randomly tests its employees throughout the yr. Last year in the 400 random tests conducted, 14 employees failed the test. Would it be reasonable to conclude that less than 5% of the employees are not able to pass the random drug test?

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