Question

In: Statistics and Probability

A national health organization warns that 30% of middle school students nation wide have been drunk....

A national health organization warns that 30% of middle school students nation wide have been drunk. A local health agency randomly surveys 100 students and only 25 report having been drunk. Construct an appropriate 80% confidence interval.

A. 0.25

B. 0.0555

C. 0.1946 to 0.3055

D. 0.1651 to 0.3349

Please show work and exaplain why. Thank you!

Expert Solution

Solution :

Given that,

n = 100

x = 25

= x / n = 25 / 100 = 0.250

1 - = 1 - 0.250 = 0.750

At 80% confidence level the z is ,

= 1 - 80% = 1 - 0.80 = 0.20

/ 2 = 0.20 / 2 = 0.10

Z_/2 = Z_0.10 = 1.282

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

= 1.282 * ( $\sqrt$ ((0.250 * 0.750) / 100)

= 0.0555

A 80 % confidence interval for population proportion p is ,

- E < P < + E

0.250 - 0.0555 < p < 0.250 + 0.0555

0.1945< p < 0.3055

Option B) is correct.

orchestra answered 2 years ago

The national health organization warns that 30% of the middle school students nationwide have been drunk....

The national health organization warns that 30% of the middle school students nationwide have been drunk. A local health agency randomly and anonymously surveys 100 of the middle school students in its city and finds that only 21 of them report having been drunk. Create a 95% confidence interval for the proportion of the city's middle school students who have been drunk. Is there any reason to believe that the national level of 30% is not true for the middle...

You have been asked by a middle school health teacher to discuss danger signs related to...

You have been asked by a middle school health teacher to discuss danger signs related to eating disorders in young people. Explain to them the types, symptoms, causes, and treatment options. What would you warn these young people about and how would you help them prevent the ego deficiencies and cognitive disturbances often associated with these disorders?

A national organization has been working with utilities throughout the nation to find sites for large...

A national organization has been working with utilities throughout the nation to find sites for large wind machines that generate electricity. Wind speeds must average more than 25 miles per hour (mph) for a site to be acceptable. Recently, the organization conducted wind speed tests at a particular site. Based on a sample of 43 wind speed recordings (taken at random intervals), the wind speed at the site averaged 25.8 mph, with a population standard deviation of 4.2 mph a....

There are 700 students in a middle school. At the end of the year, there is...

There are 700 students in a middle school. At the end of the year, there is a school-wide drawing for 3 identical new bicycles. Is this a combination or a permutation? Why? How many possible outcomes of the drawing are there? Suppose that bicycles in the drawing are not identical: One bike is plated in gold and valued significantly higher than the other two, the silver and bronze bikes, with the bronze being the cheapest. Does this change the number...

A small school has 100 students. You have been commissioned school photographer. 1. You have been...

A small school has 100 students. You have been commissioned school photographer. 1. You have been offered to photograph a model action shot for a salary of $100 on the same day as the school photos are scheduled. You can’t do both. What is the limited resource, and as what kind of cost do you consider the missed salary of this photoshoot? 2. Without calculating, do you think parents’ price elasticity of demand for photos of their children is generally...

You have been asked to participate on a committee charged with designing the ideal middle school....

You have been asked to participate on a committee charged with designing the ideal middle school. Given your knowledge of the developmental stages adolescents are traversing at this age, discuss three recommendations you would offer to promote the social, emotional, and academic development of the students and the rationale for each recommendation. (detailed answer please)

A group of researchers is interested in middle school students and their willingness to appear to...

A group of researchers is interested in middle school students and their willingness to appear to stand out. A random sample of 260 middle school students is gathered, and the researchers ask them to wear bright orange shoes to school for a day. In the sample of 260 students, 192 were willing to wear the bright orange shoes. Estimate the overall proportion of middle school students that would be willing to wear bright orange shoes to school for the day....

1. Students select a Middle Eastern nation to compare to the United States. Use the links...

1. Students select a Middle Eastern nation to compare to the United States. Use the links on the Central Bank and Monetary Authority website to research both Central Banks. 2. Students submit a paper that addresses the following areas; a. Compare and contrast when, why and how each central bank was established. b. Compare and contrast two mandates of each central bank. c. Compare and contrast the degree of autonomy and transparency of each central bank. ...

A health psychologist hypothesizes that depression levels in the nation have been decreasing over the years....

A health psychologist hypothesizes that depression levels in the nation have been decreasing over the years. In the late 2000s, the average score on the Birk Depression Inventory (BDI) in the nation was 17 with a variance of 56.25. A current sample of 16 generates an average BDI score of 13.4. What can be concluded with an α of 0.10? c) Obtain/compute the appropriate values to make a decision about H0. (Hint: Make sure to write down the null and...

A health psychologist hypothesizes that stress levels in the nation have been increasing over the years....

A health psychologist hypothesizes that stress levels in the nation have been increasing over the years. In the late 1990s, the average score on the Birk Stress Inventory (BSI) in the nation was 17 with a standard deviation of 6.2. A current sample of 29 produces a mean BSI score of 14.8. What can be concluded with an α of 0.10? a) What is the appropriate test statistic? ---Select--- na z-test one-sample t-test independent-samples t-test related-samples t-test b) Population: ---Select---...