91影视

Insurance companies are interested in knowing the population percent of drivers who always buckle up before riding in a car.

a. When designing a study to determine this population proportion, what is the minimum number you would need to survey to be $95\%$confident that the population proportion is estimated to within $0.03$?

b. If it were later determined that it was important to be more than $95\%$confident and a new survey was commissioned, how would that affect the minimum number you would need to survey? Why?

Suppose that the insurance companies did do a survey. They randomly surveyed $400$drivers and found that $320$claimed they always buckle up. We are interested in the population proportion of drivers who claim they always buckle up.

a. i. x = __________ ii. n = __________ iii. p鈥� = __________

b. Define the random variables $X$and $P\text{'}$, in words.

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

d. Construct a $95\%$confidence interval for the population proportion who claim they always buckle up. i. State the confidence interval. ii. Sketch the graph. iii. Calculate the error bound.

e. If this survey were done by telephone, list three difficulties the companies might have in obtaining random results.

According to a recent survey of 1,200 people, 61% feel that the president is doing an acceptable job. We are interested in the population proportion of people who feel the president is doing an acceptable job.

a. Define the random variables X and P鈥� in words.

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

c. Construct a 90% confidence interval for the population proportion of people who feel the president is doing an acceptable job.

i. State the confidence interval.

ii. Sketch the graph.

iii. Calculate the error bound.

Suppose the Census needed to be $98\%$ confident of the population mean length of time. Would the Census have to survey more people? Why or why not?

120. An article regarding interracial dating and marriage recently appeared in the Washington Post. Of the$1,709$randomly selected adults, $315$identified themselves as Latinos, $323$ identified themselves as blacks, $254$identified themselves as Asians, and $779$identified themselves as whites. In this survey, $86\%$of blacks said that they would welcome a white person into their families. Among Asians, $77\%$would welcome a white person into their families, $71\%$would welcome a Latino, and $66\%$would welcome a black person.

a. We are interested in finding the $95\%$confidence interval for the percent of all black adults who would welcome a white person into their families. Define the random variables role="math" localid="1650173946070" $X$and $P^{\text{'}}$, in words.

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

c. Construct a $95\%$ confidence interval.

i. State the confidence interval.

ii. Sketch the graph.

iii. Calculate the error bound.

An article regarding interracial dating and marriage recently appeared in the Washington Post. Of the $1,709$randomly selected adults, $315$identified themselves as Latinos, $323$identified themselves as blacks, $254$identified themselves as Asians, and $779$identified themselves as whites. In this survey, $86\%$of blacks said that they would welcome a white person into their families. Among Asians, $77\%$would welcome a white person into their families, $71\%$would welcome a Latino, and $66\%$would welcome a black person.

a. We are interested in finding the $95\%$confidence interval for the percent of all black adults who would welcome a white person into their families. Define the random variables $\mathrm{X}$and ${\mathrm{P}}^{\text{'}}$, in words.

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

c. Construct a $95\%$confidence interval.

i. State the confidence interval.

ii. Sketch the graph.

iii. Calculate the error bound.

Refer to the information in Exercise 8.120.

a. Construct three 95% confidence intervals.

i. percent of all Asians who would welcome a white person into their families.

ii. percent of all Asians who would welcome a Latino into their families.

iii. percent of all Asians who would welcome a black person into their families.

b. Even though the three-point estimates are different, do any of the confidence intervals overlaps? Which?

c. For any intervals that do overlap, in words, what does this imply about the significance of the differences in the true proportions?

d. For any intervals that do not overlap, in words, what does this imply about the significance of the differences in the true proportions?

122. Stanford University conducted a study of whether running is healthy for men and warner overage $50$. During the first eight years of the study, $1.5\%$of the $451$members of the $50$-Plus Fatness Association died. We are interested in the proportion of people over $50$who ran and tied in the same eight-year period.

a. Define the random variables$XandF$in words.

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

c. Construct a $97\%$confidence interval for the population proportion of people average$50$ we ran and died in the same eight-year period.

i. State the confidence interval.

ii. Sketch the graph.

iii. Calculate the error bound.

d. Explain what a " $97\%$confidence interval" means for this study.

A telephone poll of 1,000 adult Americans was reported in an issue of Time Magazine. One of the questions asked was 鈥淲hat is the main problem facing the country?鈥� Twenty per cent answered 鈥渃rime.鈥� We are interested in the population proportion of adult Americans who feel that crime is the main problem.

a. Define the random variables X and P鈥� in words.

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 feel that crime is the main problem.

i. State the confidence interval.

ii. Sketch the graph.

iii. Calculate the error bound.

d. Suppose we want to lower the sampling error. What is one way to accomplish that?

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

A telephone poll of $1000$adult Americans was reported in an issue of Time Magazine. Another question in the poll was 鈥淸How much are] you worried about the quality of education in our schools?鈥� Sixty-three percent responded 鈥渁 lot鈥�. We are interested in the population proportion of adult Americans who are worried a lot about the quality of education in our schools.

a. Define the random variables $X$and $P鈥�$in words.

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 Yankelevich Partners, Inc. (which conducted the poll) is $卤3\%$. In one to three complete sentences, explain what the $卤3\%$ represents.