Exam 7: Estimating Parameters and Determining Sample Sizes

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 laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was 185 milligrams with s=17.6 milligrams. A confidence interval of $173.8 \mathrm { mg } < \mu < 196.2 \mathrm { mg }$ is constructed for the true mean cholesterol content of all such eggs. It was assumed that the population has a normal distribution. What confidence level does this interval represent?

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.

Express the confidence interval (0.432,0.52) in the form of $\hat { p } \pm \mathrm { E }$

The margin of error ________ ________ (increases or decreases)with an increase in confidence level.

Define in as clear language as possible how a 95% confidence interval can be used for hypothesis tests.

Bert constructed a confidence interval to estimate the mean weight of students in his class. The population was very small - only 30. Ruth constructed a confidence interval for the mean weight of all adult males in the city. She based her confidence interval on a very small sample of only 5. Which confidence interval is likely to give a better estimate of the mean it is estimating? Which is likely to be more of a problem, a small sample or a small population?

To be able to say with 95% confidence that the standard deviation of a data set is within 10% of the population's standard deviation, the number of observations within the data set must be Greater than or equal to what quantity?

How do you determine whether to use the z or t distribution in computing the margin of error, $E = z _ { \alpha / 2 } \cdot \frac { \sigma } { \sqrt { n } } \text { or } E = t _ { \alpha / 2 } \cdot \frac { s } { \sqrt { n } } ?$

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. $n = 195 , x = 162 ; 95 \%$ confidence

Use the given data to find the minimum sample size required to estimate the population proportion. Margin of error: 0.008 ; confidence level: 98% $\hat { p } \text { and } \hat { q }$ unknown

A 99% confidence interval (in inches) for the mean height of a population is $65.7 < \mu < 67.3$ This result is based on a sample of size 144 . Construct the 95% confidence interval. (Hint: you will first need to find the sample mean and sample standard deviation).

Use the given data to find the minimum sample size required to estimate the population proportion. Margin of error: 0.028; confidence level: 99%; p and q unknown

A survey of 300 union members in New York State reveals that 112 favor the Republican candidate for governor. Construct the 98% confidence interval for the true population Proportion of all New York State union members who favor the Republican candidate.

Which of the following critical values is appropriate for a 98% confidence level where n=7 ; $\sigma = 27$ and the population appears to be normally distributed.

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. Thirty randomly selected students took the calculus final. If the sample mean was 95 and the standard deviation was 6.6 , construct a 99% confidence interval for the mean score of all students.

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 laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was 185 milligrams with s=17.6 milligrams. Construct a 95% confidence interval for the true mean cholesterol content of all such eggs.

A group of 59 randomly selected students have a mean score of 29.5 with a standard deviation of 5.2 on a placement test. What is the 90% confidence interval for the mean score, $\mu$ , of all students taking the test?

4)Find the critical value $\chi _ { \mathrm { R } } ^ { 2 }$ corresponding to a sample size of 19 and a confidence level of 99 percent.