Exam 7: Estimating Parameters and Determining Sample Sizes

Use the given data to find the minimum sample size required to estimate the population proportion. -Margin of error: 0.07; confidence level: 90%; from a prior study, $\hat { p }$ is estimated by 0.30.

Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation σ. Assume that the population has a normal distribution. Round the confidence interval limits to the same number of decimal places as the sample standard deviation. -A sociologist develops a test to measure attitudes about public transportation, and 27 randomly selected subjects are given the test. Their mean score is 76.2 and their standard deviation is 21.4. Construct the 95% Confidence interval for the standard deviation, σ, of the scores of all subjects.

Use the given data to find the minimum sample size required to estimate the population proportion. -Margin of error: 0.008; confidence level: 95%; $\hat { p } \text { and } \hat { q } \text { unknown }$

Find the value of ${ } ^ { z } \alpha / 2$ that corresponds to a confidence level of 89.48%.

Use the confidence level and sample data to find a confidence interval for estimating the population µ. Round your answer to the same number of decimal places as the sample mean. -A laboratory tested 82 chicken eggs and found that the mean amount of cholesterol was 228 milligrams with $\sigma$ = 19.0 milligrams. Construct a 95% confidence interval for the true mean cholesterol content, $\mu$ of all such eggs.

Do one of the following, as appropriate: (a) Find the critical value $\mathrm { z } _ { \alpha / 2 }$ , (b) find the critical value $t _ { \alpha / 2 }$ , (c) state that neither the normal nor the t distribution applies. - $90 \% ; \mathrm { n } = 9 ; \sigma = 4.2 ;$ population appears to be very skewed.

Use the given degree of confidence and sample data to construct a confidence interval for the population mean $\mu$ . Assume that the population has a normal distribution. -A sociologist develops a test to measure attitudes towards public transportation, and 27 randomly selected subjects are given the test. Their mean score is 76.2 and their standard deviation is 21.4. Construct the 95% Confidence interval for the mean score of all such subjects.

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. -Of 260 employees selected randomly from one company, 18.46% of them commute by carpooling. Construct a 90% confidence interval for the true percentage of all employees of the company who carpool.

Find the degree of confidence used in constructing the confidence interval $0.523 < p < 0.669$ for the population proportion $p$ using sample data with $n = 109 , x = 65$ .

Solve the problem. -In a certain population, body weights are normally distributed with a mean of 152 pounds and a standard deviation of 26 pounds. How many people must be surveyed if we want to estimate the percentage who weigh More than 180 pounds? Assume that we want 96% confidence that the error is no more than 4 percentage points.

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. -n = 56, x = 30; 95% confidence

Use the confidence level and sample data to find a confidence interval for estimating the population µ. Round your answer to the same number of decimal places as the sample mean. -A random sample of 104 light bulbs had a mean life of $\bar { x } = 543$ hours with a standard deviation of $\sigma = 26$ hours. Construct a $90 \%$ confidence interval for the mean life, $\mu$ , of all light bulbs of this type.

Express the confidence interval using the indicated format. -Express the confidence interval $0.491 \pm 0.057$ in the form of $\hat { p } - \mathrm { E } < \mathrm { p } < \hat { \mathrm { p } } + \mathrm { E }$ .

Express the confidence interval $0.039 < p < 0.479 \text { in the form of } \hat { p } \pm \mathrm { E }$

Of 118 randomly selected adults, 34 were found to have high blood pressure. Construct a 95% confidence interval for the true percentage of all adults that have high blood pressure.

Use the given degree of confidence and sample data to construct a confidence interval for the population mean $\mu$ . Assume that the population has a normal distribution. -A savings and loan association needs information concerning the checking account balances of its local customers. A random sample of 14 accounts was checked and yielded a mean balance of $664.14 and a standard Deviation of $297.29. Find a 98% confidence interval for the true mean checking account balance for local Customers.

Use the given information to find the minimum sample size required to estimate an unknown population mean $\mu$ -Margin of error: $135, confidence level: 95%, $\sigma = \$ 500$

Find the critical value $\mathrm { z } _ { \alpha / 2 }$ that corresponds to a 98% confidence level.

Use the given data to find the minimum sample size required to estimate the population proportion. - $\text { Margin of error: } 0.018 \text {; confidence level: } 99 \% ; \hat { \mathrm { p } } \text { and } \hat { \mathrm { q } } \text { unknown }$

Draw a diagram of the chi-square distribution. Discuss its shape and values.