/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q 4E A random sample of 90 observatio... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Q 4E (page 338)

A random sample of 90 observations produced a mean x = 25.9 and a standard deviation s = 2.7.

a. Find an approximate 95% confidence interval for the population mean渭

b. Find an approximate 90% confidence interval for渭

c. Find an approximate 99% confidence interval for渭

Short Answer

Expert verified

The standard deviation is commonly utilized as a measurement of an asset's comparative volatility. The standard deviation is determined as the square root of the variation by calculating the departure of every observation point from the mean.

Step by step solution

01

(a) The data is given below

Sample sizen=90X=25.9s=2.7

Here, the population standard deviation is known in this case, we use the t interval.

Degrees of freedom = n-1=90-1=89

The formula is given below:

X-E,X炉+E

Given the error in the margin

E=tc脳sntc=1.986

E=1.986脳2.790=5.36229.486833=0.565226

The confidence interval is: 25.9-0.565226, 25.9 + 0.565226=>25.3348,26.4652

02

(b) The data is given below

The formula is given below:

X-E,X炉+E

Given the error in the margin

E=tc脳sntc=1.662

E=1.662脳2.790=4.48749.486833=0.473013

The confidence interval is:25.9-0.473013, 25.9 + 0.473013= >25.4270,26.3730

03

(c) The data is given below

The formula is given below:

蠂-E,蠂+E

Given the error in the margin

E=tc脳sntc=1.662E=2.632脳2.790=7.10649.486833=0.74908

The confidence interval is: (25.1509, 26.6491)

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Monitoring phone calls to a toll-free number. A largefood-products company receives about 100,000 phone callsa year from consumers on its toll-free number. A computermonitors and records how many rings it takes for an operatorto answer, how much time each caller spends 鈥渙n hold,鈥� andother data. However, the reliability of the monitoring systemhas been called into question by the operators and their labour unions. As a check on the computer system, approximatelyhow many calls should be manually monitored during thenext year to estimate the true mean time that callers spend onhold to within 3 seconds with 95% confidence? Answer thisquestion for the following values of the standard deviation ofwaiting times (in seconds): 10, 20, and 30.

Eye shadow, mascara, and nickel allergies. Pigmented makeup products like mascara and eye shadow may contain metal (e.g., nickel) allergens. Is a nickel allergy more likely to occur in women who report cosmetic dermatitis from using eye shadow or mascara? This was the question of interest in a paper published in the Journal of the European Academy of Dermatology and Venereology (June 2010). In a sample of 131 women with cosmetic dermatitis from using eye shadow, 12 were diagnosed with a nickel allergy. In a sample of 250 women with cosmetic dermatitis from using mascara, 25 were diagnosed with a nickel allergy.

a. Compute a 95% confidence interval for the proportion of women with cosmetic dermatitis from using eye shadow who have a nickel allergy. Interpret the result.

b. Compute a 95% confidence interval for the proportion of women with cosmetic dermatitis from using mascara who have a nickel allergy. Interpret the result.

c. Suppose you are informed that the true proportion with a nickel allergy for one of the two groups (eye shadow or mascara) is .12. Can you determine which group is referenced? Explain.

General health survey. The Centres for Disease Control and Prevention (CDCP) in Atlanta, Georgia, conducts an annual survey of the general health of the U.S. population as part of its Behavioural Risk Factor Surveillance System. Using random-digit-dialing, the CDCP telephones U.S. citizens over 18 years of age and asks them the following four questions:

1. Is your health generally excellent, very good, good, fair, or poor?

2. How many days during the previous 30 days was your physical health not good because of injury or illness?

3. How many days during the previous 30 days was your mental health not good because of stress, depression, or emotional problems?

4. How many days during the previous 30 days did your physical or mental health prevent you from performing your usual activities?

Identify the parameter of interest for each question

U.S. Postal Service鈥檚 performance. The U.S. Postal Service (USPS) reports that 95% of first-class mail within the same city is delivered on time (i.e., within 2 days of the time of mailing). To gauge the USPS performance, Price Waterhouse monitored the delivery of first-class mail items between Dec. 10 and Mar. 3鈥攖he most difficult delivery season due to bad weather conditions and holidays. In a sample of 332,000 items, Price Waterhouse determined that 282,200 were delivered on time. Comment on the performance of USPS first-class mail service over this time period.

Suppose you want to estimate a population proportion,,pand,p^=.42,N=6000andn=1600.Find an approximate 95% confidence interval forp.
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.