# 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.

#### Solution Summary

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