Exam 7: Estimating Parameters and Determining Sample Sizes

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 μ 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

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.

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

Why is $s ^ { 2 }$ the best point estimate of $\boldsymbol { \sigma } ^ { 2 }$ ?

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

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

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 .

Under what circumstances can you replace $\sigma$ with s in the formula $E = z _ { a / 2 } \cdot \frac { \sigma } { \sqrt { n } } ?$

Based on a simple random sample of students from her school, Sally obtained a point estimate of the mean weight of students at her school. What additional information would be provided by a confidence interval estimate of the mean weight?

You want to estimate σ for the population of waiting times at McDonald's drive-up windows, and you want to be 95% confident that the sample standard deviation is with 20% of $\sigma$ Find the minimum sample size. Is this sample size practical?

You want to be 95% confident that the sample variance is within 40% of the population variance. Find the appropriate minimum sample size.

Fill in the blank: The critical value $z _ { \alpha / 2 }$ that corresponds to a _________% confidence level is 2.33.

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

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

Identify the distribution that applies to the following situation: In constructing a confidence interval of ? , you have 50 sample values and they appear to be From a population with a skewed distribution. The population standard deviation is not Known. ______________

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

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

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.

In a Gallup poll, 1011 adults were asked if they consume alcoholic beverages and 64% of them said that they did. Construct a 90% confidence interval estimate of the proportion of all adults who consume alcoholic beverages. Can we safely conclude that the majority of adults consume alcoholic beverages?

Which critical value is appropriate for a 99 % confidence level where n=17 ; $\sigma$ is unknown and the population appears to be normally distributed?