91影视

124. Refer to Exercise 8.123. Another question in the poll was "[How much are) you worried about the quality of education in our schools?" Sixty-three percent responded "a lot". We are interested in the population proportion of adult Americans who are worried a lot about the quality of education in our schools.

$Xand{P}^{\text{'}}$

b. Which distribution should you use for this problem? Explain your choice.

c. Construct a $95\%$ confidence interval for the population proportion of adult Americans who are worried a lot about the quality of education in our schools.

i. State the confidence interval.

ii. Sketch the graph.

iii. Calculate the error bound.

d. The sampling error given by Yanklovich Partners, Inc. (which conducted the poll) is $卤3\%$. In one to three complete sentences, explain what the $卤3\%$ represents.

Use the following information to answer the next three exercises: According to a Field Poll, 79% of California adults (actual results are 400 out of 506 surveyed) feel that 鈥渆ducation and our schools鈥� is one of the top issues facing California. We wish to construct a 90% confidence interval for the true proportion of California adults who feel that education and the schools are one of the top issues facing California.

A point estimate for the true population proportion is:

a. 0.90

b. 1.27

c. 0.79

d. 400

Use the following information to answer the next two exercises: Five hundred and eleven $\left(511\right)$homes in a certain southern California community are randomly surveyed to determine if they meet minimal earthquake preparedness recommendations. One hundred seventy-three $\left(173\right)$of the homes surveyed met the minimum recommendations for earthquake preparedness, and $338$did not.

Find the confidence interval at the $90\%$Confidence Level for the true population proportion of southern California community homes meeting at least the minimum recommendations for earthquake preparedness.

a. $(0.2975,0.3796)$

b.$(0.6270,0.6959)$

c. $(0.3041,0.3730)$

d.$(0.6204,0.7025)$

A sample of $20$heads of lettuce was selected. Assume that the population distribution of head weight is normal. The weight of each head of lettuce was then recorded. The mean weight was $2.2$pounds with a standard deviation of $0.1$pounds. The population standard deviation is known to be $0.2$pounds.

Identify the following:

a. $\stackrel{炉}{x}=$

b. $蟽=$

C. $n=$

On May $23,2013$, Gallup reported that of the $1005$people surveyed, $76\%$of U.S. workers believe that they will continue working past retirement age. The confidence level for this study was reported at $95\%$with a $卤3\%$margin of error.

a. Determine the estimated proportion from the sample.

b. Determine the sample size.

c. Identify CL and .

d. Calculate the error bound based on the information provided.

e. Compare the error bound in part d to the margin of error reported by Gallup. Explain any differences between the values.

f. Create a confidence interval for the results of this study.

g. A reporter is covering the release of this study for a local news station. How should she explain the confidence interval to her audience?

A national survey of 1,000 adults was conducted on May 13, 2013, by Rasmussen Reports. It concluded with 95% confidence that 49% to 55% of Americans believe that big-time college sports programs corrupt the process of higher education.

a. Find the point estimate and the error bound for this confidence interval.

b. Can we (with 95% confidence) conclude that more than half of all American adults believe this?

c. Use the point estimate from part a and n = 1,000 to calculate a 75% confidence interval for the proportion of American adults that believe that major college sports programs corrupt higher education.

d. Can we (with 75% confidence) conclude that at least half of all American adults believe this

132. Public Policy Polling recently conducted a survey asking adults across the U.S. about music preferences. When asked, $80$ of the $571$ participants admitted that they have illegally downloaded music.

a. Create a $99\%$ confidence interval for the true proportion of American adults who have illegally downloaded music.

b. This survey was conducted through automated telephone interviews on May 6 and 7,2013. The error bound of the survey compensates for sampling error or natural variability among samples. List some factors that could affect the survey's outcome that is not covered by the margin of error.

c. Without performing any calculations, describe how the confidence interval would change if the confidence level changed from $99\%to90\%$.

You plan to conduct a survey on your college campus to learn about the political awareness of students. You want to estimate the true proportion of college students on your campus who voted in the 2012 presidential election with 95% confidence and a margin of error no greater than five per cent. How many students must you interview?

In a recent Zogby International Poll, nine of 48 respondents rated the likelihood of a terrorist attack in their community as 鈥渓ikely鈥� or 鈥渧ery likely.鈥� Use the 鈥減lus-four鈥� method to create a 97% confidence interval for the proportion of American adults who believe that a terrorist attack in their community is likely or very likely. Explain what this confidence interval means in the context of the problem.