Question

In: Statistics and Probability

A recent survey on the usage of cosmetics among youth provided the following data: Year: 2004;...

A recent survey on the usage of cosmetics among youth provided the following data:

Year: 2004; Sample size: 5000; Youth who use cosmetics: 36%
Year: 2014; Sample size: 4250; Youth who use cosmetics: 47%

Construct a 99% confidence interval for the difference in population proportions of youth who were using cosmetics in 2004 and youth who were using cosmetics in 2014. Assume that random samples are obtained and the samples are independent. (Round your answers to three decimal places.)

z0.10	z0.05	z0.025	z0.01	z0.005
1.282	1.645	1.960	2.326	2.576

Select the correct answer below:

(−0.150,−0.070)

(−0.136,−0.084)

(−0.140,−0.080)

(−0.127,−0.093)

Expert Solution

The confidence interval for difference in proportions is

P1 - P2 +- Z/2 * ((P1 * Q1) / n1 + (P2 * Q2) / n2

Here P1 = 36% = 0.36 youth who use cosmetics in 2004

Q1 = 1 - P1 = 1 - 0.36 = 0.64

n1 = 5000

Here P2 = 47% = 0.47 youth who use cosmetics in 2014

Q2 = 1 - P2 = 1 - 0.47 = 0.53

n2 = 4250

Confidence interval = 99%, So = 0.01 and /2 = 0.005

So Z0.005 = 2.576 as given in the data

SO the confidecne interval for difference in the proportions = P1 - P2 +- Z/2 * ((P1 * Q1) / n1 + (P2 * Q2) / n2 )

= 0.36 - 0.47 +- 2.576 * (0.36 * 0.64) / 5000 + (0.47 * 0.53) / 4250

= -0.11 +- 2.576 * 0.0001

= -0.11 +- 2.576 * 0.01

= -0.11 +-0.0258

(-0.136 , -0.084)

So the Answer is B

orchestra answered 1 year ago

Results on seat belt usage from the 2003 Youth Risk Behavior Survey were published in a...

Results on seat belt usage from the 2003 Youth Risk Behavior Survey were published in a USA Snapshot on January 13, 2005. The following table outlines the results from the high school students who were surveyed in the state of Nebraska. They were asked whether or not they rarely or never wear seat belts when riding in someone else's car. Using α = .05, does this sample present sufficient evidence to reject the hypothesis that gender is independent of seat...

1A) Results on seat belt usage from the 2003 Youth Risk Behavior Survey were published in...

1A) Results on seat belt usage from the 2003 Youth Risk Behavior Survey were published in a USA Snapshot on January 13, 2005. The following table outlines the results from the high school students who were surveyed in the state of Nebraska. They were asked whether or not they rarely or never wear seat belts when riding in someone else's car. Using α = .05, does this sample present sufficient evidence to reject the hypothesis that gender is independent of...

The following data has been provided for a company’s most recent year of operations: Return on...

The following data has been provided for a company’s most recent year of operations: Return on investment 30 % Average operating assets $ 75,000 Minimum required rate of return 17 % The residual income for the year was closest to: $9,750 $20,000 $15,750 $21,500

Read the Following Case Scenario: A recent survey was taken among employees at Biotech Health and...

Read the Following Case Scenario: A recent survey was taken among employees at Biotech Health and Life Products (Biotech). The results were alarming, as it appeared the leadership has been less effective than in the past. Some of the common complaints seemed to focus on the lack of vision, a breakdown in communication and a lack of connection with staff. You have read the results and as Vice President of Biotech, you completely agree with employees. Leadership is the cornerstone...

Bitonti Corporation has provided the following data for its most recent year of operation: Manufacturing costs:...

Bitonti Corporation has provided the following data for its most recent year of operation: Manufacturing costs: Variable manufacturing cost per unit produced: Direct materials $ 9 Direct labor $ 7 Variable manufacturing overhead $ 5 Fixed manufacturing overhead per year $ 156,000 Selling and administrative expenses: Variable selling and administrative expense per unit sold $ 5 Fixed selling and administrative expense per year $ 81,000 Units in beginning inventory 0 Units produced during the year 12,000 Units sold during the...

One recent survey of cell phone usage around the world showed that only 4 percent of...

One recent survey of cell phone usage around the world showed that only 4 percent of people in countries like Uganda and Ethiopia have access to a smartphone. Explain how this presents an opportunity for these countries to attain faster growth. What are the likely costs of economic growth? Suppose that you are currently getting your undergraduate degree and are considering going on for a graduate degree. You expect that once you have your graduate degree, your income and your...

. A recent drug survey showed an increase in the use of drugs and alcohol among...

. A recent drug survey showed an increase in the use of drugs and alcohol among local high school seniors as compared to the national percent. Suppose that a survey of 100 local seniors and 100 national seniors is conducted to see if the proportion of drug and alcohol use is higher locally than nationally. Locally, 65 seniors reported using drugs or alcohol within the past month, while 60 national seniors reported using them. Ho: p1 = p2 ...

The data can find in potuse (faraway package). The national Youth Survey collected a sample of...

The data can find in potuse (faraway package). The national Youth Survey collected a sample of 11-17 year-olds with 117 boys and 120 girls, asking questions about marijuana usage. This data is actually longitudinal – the same boys and girls are followed for five years. However, for the purposes of this question, imagine that the data is cross-sectional, that is, a different sample of boys and girls are sampled each year. Build a model for the different levels of marijuana...

In a recent survey, the following data were obtained in response to the question “When making...

In a recent survey, the following data were obtained in response to the question “When making a purchase, do you prefer to pay with cash or a credit card?” The responses are listed in the table. Gender Cash Credit Card Total Males 21 39 60 Females 15 25 40 Total 36 64 100 What is the probability that a randomly selected person is a female and prefers to pay with cash?

A recent drug survey showed an increase in the use of drugs and alcohol among local...

A recent drug survey showed an increase in the use of drugs and alcohol among local high school seniors as compared to the national percent. Suppose that a survey of 100 local seniors and 100 national seniors is conducted to see if the proportion of drug and alcohol use is higher locally than nationally. Locally, 67 seniors reported using drugs or alcohol within the past month, while 63 national seniors reported using them. Conduct a hypothesis test at the 5%...