Question

In: Statistics and Probability

The National AIDS Behavioral Surveys interviewed a sample of adults in cities where AIDS is most...

The National AIDS Behavioral Surveys interviewed a sample of adults in cities where AIDS is most common. This sample included 803 heterosexuals who reported having more than one sexual partner in the past year. We can consider this an SRS of size 803 from the population of all heterosexuals in high-risk cities who have multiple partners. These people risk infection with the AIDS virus. Yet 304 of the respondents said they never use condoms.

Find a 95% confidence interval for the population proportion that never use condoms?

Expert Solution

Solution :

Given that,

n = 803

x = 304

Point estimate = sample proportion = = x / n = 304/803=0.379

1 - = 1- 0.379 =0.621

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96 ( Using z table )

Margin of error = E = Z/2 * $\sqrt$ ((( * (1 - )) / n)

= 1.96 ( $\sqrt$ ((0.379*0.621) /803 )

E = 0.0336

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.379-0.0336 < p <0.379+ 0.0336

0.3454< p < 0.4126

The 95% confidence interval for the population proportion p is : 0.3454, 0.4126

orchestra answered 1 year ago

National surveys are frequently conducted by asking a number of several thousand adults throughout the nation...

National surveys are frequently conducted by asking a number of several thousand adults throughout the nation and using these data to infer the opinion of the nation's adults. Explain which set forms the population and which form the sample. Cite an example from a newspaper, TV or Internet. Say the topic of the survey, the population, the sample and the result.. Cite an example from a newspaper, TV or Internet. Say the topic of the survey, the population, the sample...

A national survey conducted among a simple random sample of 1513 adults shows that 835 of...

A national survey conducted among a simple random sample of 1513 adults shows that 835 of Americans think the Civil War is still relevant to American politics and the political life. Conduct a hypothesis test to determine if these data provide strong evidence that the majority of the Americans think the Civil War is still relevant. Give answers to at least 4 decimal places. A)Identify the claim B)What are the correct hypotheses? (Select the correct symbols and use decimal values...

The National Coffee Association reported that 64% of U.S. adults drink coffee daily. A random sample...

The National Coffee Association reported that 64% of U.S. adults drink coffee daily. A random sample of 225 U.S. adults is selected. Round your answers to at least four decimal places as needed. Find the probability that less than 59% of the sampled adults drink coffee daily.

The National Coffee Association reported that 63% of U.S. adults drink coffee daily. A random sample...

The National Coffee Association reported that 63% of U.S. adults drink coffee daily. A random sample of 300 U.S. adults is selected. Round your answers to at least four decimal places as needed. Find probability that less then 58% of sampled adults drink coffee daily

2 The Civil War. A national survey conducted among a simple random sample of 1,507 adults...

2 The Civil War. A national survey conducted among a simple random sample of 1,507 adults shows that 56% of Americans think the Civil War is still relevant to American politics and political life. (a) Conduct a hypothesis test to determine if these data provide strong evidence that the majority of the Americans think the Civil War is still relevant. (b) Interpret the p-value in this context. (c) Calculate a 90% confidence interval for the proportion of Americans who think...

The following regression was run using a sample of 656 municipalities in Brazil, where the national...

The following regression was run using a sample of 656 municipalities in Brazil, where the national government allocated personnel randomly to permit National Government Audit Teams to audit and publish local government finances (the taxes and spending of municipalities). The variable audit# is the number of accountants assigned to be part of the team (the average team was 4 people, but some teams were 0 and large teams were 10) and voteshare is the vote share received by the incumbent...

In a sample of 800 U.S. adults, 199 think that most celebrities are good role models....

In a sample of 800 U.S. adults, 199 think that most celebrities are good role models. Two Two U.S. adults are selected at random from the population of all U.S. adults without replacement. Assuming the sample is representative of all U.S. adults, complete parts (a) through (c). (a) Find the probability that both adults think most celebrities are good role models. The probability that both adults think most celebrities are good role models is ________?(Round to three decimal places as...

In 2012, the General Social Survey asked a random sample of adults, "Compared to most people,...

In 2012, the General Social Survey asked a random sample of adults, "Compared to most people, how informed are you about politics?" Suppose that the following are the data classified by their responses to this question and their age group (the data has been modified slightly for testing purposes): Not at All A little Somewhat Very Extremely Age 20-29 7 29 28 13 0 Age 30-39 16 29 56 22 8 Age 40-49 3 24 50 26 14 Age 50...

In a sample of 1100 U.S. adults, 203 think that most celebrities are good role models. Two...

In a sample of 1100 U.S. adults, 203 think that most celebrities are good role models. Two Two U.S. adults are selected at random from the population of all U.S. adults without replacement. Assuming the sample is representative of all U.S. adults, complete parts (a) through (c). (a) Find the probability that both adults think most celebrities are good role models. The probability that both adults think most celebrities are good role models is ________?(Round to three decimal places as needed.)...

The most common experimental technique to perform elemental analysis is combustion analysis, where a sample is...

The most common experimental technique to perform elemental analysis is combustion analysis, where a sample is burned in a large excess of oxygen and the combustion products are trapped in a variety of ways. A 99.99% pure, 0.4831 g sample containing only carbon, hydrogen, and nitrogen is subjected to combustion analysis, resulting in the formation of 1.353 g CO2, 0.2750 g H2O, and 0.1833 g NO. What is the empirical formula of the sample?