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 proportion p. n=130, x=69 ; 90% confidence

In general, what does "degrees of freedom" refer to? Find the degrees of freedom for the given information, assuming that you want to construct a confidence interval estimate of $\mu :$ Six human skulls from around 4000 B.C. were measured, and the lengths have a mean of 94.2 mm and a standard deviation of 4.9 mm.

Use the given degree of confidence and sample data to construct a confidence interval for the population mean μ. 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.

Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given statistics and confidence level. Round the margin of error to four decimal places. 98% confidence; the sample size is 800, of which 40% are successes

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 .

In constructing a confidence interval for $\sigma$ or $\sigma ^ { 2 }$ , a table is used to find the critical values $\chi _ { \mathrm { L } } ^ { 2 } \text { and } \chi _ { \mathrm { R } } ^ { 2 }$ for values of $n \leq 101$ For larger values of n, $\chi _ { \mathrm { L } } ^ { 2 } \text { and } \chi _ { \mathrm { R } } ^ { 2 }$ can be approximated by using the following formula: $\chi ^ { 2 } = \frac { 1 } { 2 } \pm z _ { \alpha / 2 } + \sqrt { 2 k - 1 } ^ { 2 }$ where k is the number of degrees of freedom and $z _ { \alpha / 2 }$ is the critical z-score. Construct the 90 % confidence interval for $\sigma$ using the following sample data: a sample of size n=232 yields a mean weight of 154 lb and a standard deviation of 25.5 lb. Round the confidence interval limits to the nearest hundredth.

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.

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

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

Define margin of error. Explain the relation between the confidence interval and the margin of error. Suppose a confidence interval is $9.65 < \mu < 11.35$ Redefine the confidence interval into a format using the margin of error and the point estimate of the population mean.

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.

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

To find the standard deviation of the diameter of wooden dowels, the manufacturer measures 19 randomly selected dowels and finds the standard deviation of the sample to be s=0.16 . Find the 95 % confidence interval for the population standard deviation $\sigma$

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

Describe the steps for finding a confidence interval

Identify the correct distribution (z, t, or neither)for each of the following Identify the correct distribution (z,t , or neither) for each of the following. Sample Size Standard Deviation Shape of the Distribution z or t or neither n=35 s=4.5 Somewhat skewed n=20 s=4.5 Bell shaped n=35 \sigma=4.5 Bell shaped n=20 \sigma=4.5 Extremely skewed

Find the critical value $z _ { \alpha / 2 }$ that corresponds to a 91% confidence level.

Interpret the following 95 % confidence interval for mean weekly salaries of shift managers at Guiseppe's Pizza and Pasta. $325.80 < \mu < 472.30$

Express a confidence interval defined as (0.432,0.52) in the form of the point estimate _____ $\pm$ the margin of error______ Express both in three decimal places.

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 $173.8 \mathrm { mg } < \mu < 196.2$ 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?