Exam 7: Estimating Parameters and Determining Sample Sizes

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

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).

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

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?

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 σ. Find the minimum sample size. Is this sample size practical?

A one-sided confidence interval for p can be written as $p < \hat { p } + \mathrm { E } \text { or } p > \hat { p } - \mathrm { E }$ where the margin of error E is modified by replacing $z _ { \alpha / 2 }$ with $Z _ { \alpha }$ If a teacher wants to report that the fail rate on a test is at most x with 90 % confidence, construct the appropriate one -sided confidence interval. Assume that a simple random sample of 74 students results in 8 who fail the test.

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 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.

When determining the sample size needed to achieve a particular error estimate you need to know $\sigma$ What are two methods of estimating $\sigma$ if $\sigma$ is unknown?

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?

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. 95% confidence; n=2388, x=1672

If the computed minimum sample size n needed for a particular margin of error is not a whole number, round the value of n _____ (up or down) to the next _____ (smaller or larger) whole number.

Identify the distribution that applies to the following situation: In constructing a confidence interval of σ you have 50 sample values and they appear to be from a population with a skewed distribution.

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?

A laboratory tested 82 chicken eggs and found that the mean amount of cholesterol was 228 milligrams with $\sigma = 19.0 \text { milligrams. }$ Construct a 95% confidence interval for the true mean cholesterol content, $\mu$ of all such eggs.

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.

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

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. If you want to construct a 95% confidence interval estimate of the mean length of skulls, what requirements must be satisfied?

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?