Exam 7: Estimating Parameters and Determining Sample Sizes

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. -90% confidence; the sample size is 1510, of which 35% are successes

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. -When 328 college students are randomly selected and surveyed, it is found that 122 own a car. Find a 99% confidence interval for the true proportion of all college students who own a car.

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, $\mu _ { e }$ , of all students taking the test?

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 proportion p. -A survey of 865 voters in one state reveals that 408 favor approval of an issue before the legislature. Construct the 95% confidence interval for the true proportion of all voters in the state who favor approval.

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?

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. - $90 \% ; \mathrm { n } = 10 ; \sigma$ is unknown; population appears to be normally distributed.

In a Gallup poll of 557 randomly selected adults, 284 said that they were underpaid. Identify the best point estimate of the percentage of adults who say they are underpaid. Construct a 95% confidence interval estimate of the percentage of adults who say that that they are underpaid. Can we safely conclude that the majority of adults say that they are underpaid?

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. -95% confidence; n = 380, x = 50

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

Solve the problem. -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).

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

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?

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. -In a clinical test with 1600 subjects, 800 showed improvement from the treatment. Find the margin of error for the 99% confidence interval used to estimate the population proportion.

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

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. - $95 \% ; \mathrm { n } = 11 ; \sigma$ is known; population appears to be very skewed.

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?

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. -n = 109, x = 65; 88% confidence

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 $\mu ; n = 9 ; \sigma = 4.2$ ; population appears to be very skewed.

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