/*! 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. T10.12 A random sample of 100聽of last ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Q. T10.12 (page 699)

A random sample of 100of last year鈥檚 model of a certain popular car found that 20had a specific minor defect in the brakes. The automaker adjusted the production process to try to reduce the proportion of cars with the brake problem. A random sample of 350of this year鈥檚 model found that 50had the minor brake defect.

a. Was the company鈥檚 adjustment successful? Carry out an appropriate test to support your answer. b. Based on your conclusion in part (a), which mistake鈥攁 Type I error or a Type II error鈥攃ould have been made? Describe a possible consequence of this error.

Short Answer

Expert verified

a. The answer isP=P(Z>1.39)=P(Z<-1.39)=0.0823

b. Failure to reject the null hypothesis is a type II mistake.

Step by step solution

01

Part (a) Step 1: Given information

We have to tell about was the company鈥檚 adjustment successful

02

Part (a) Step 2: Explanation

It has been given that

x1=20,x2=50,n1=100,n2=350

p^2=x2n2=50350鈮�0.1429

z=p^1-p^2p^p1-p^p1n1+1n2=0.2-0.14290.1556(1-0.1556)1100+1350鈮�1.39

The values using the table

P=P(Z>1.39)=P(Z<-1.39)=0.0823

03

Part (b) Step 1: Given information

We have to tell possible consequence of this error.

04

Part (b) Step 2: Explanation

The null hypothesis H was not rejected.

  • Type I blunder: H should be rejected as a null hypothesis, if H 0H is true as the null hypothesis.

Failure to reject the null hypothesis is a type II mistake.

If the null hypothesis H is false, then

It's only feasible that we made.

  • Type II error because we didn't reject the null hypothesis H .

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

An agricultural station is testing the yields for six different varieties of seed corn. The station has four large fields available, located in four distinctly different parts of the county. The agricultural researchers consider the climatic and soil conditions in the four parts of the county as being quite different, but are reasonably confident that the conditions within each field are fairly similar throughout. The researchers divide each field into six sections and then randomly assign one variety of corn seed to each section in that field. This procedure is done for each field. At the end of the growing season, the corn will be harvested, and the yield (measured in tons per acre) will be compared. Which one of the following statements about the design is correct?

a. This is an observational study because the researchers are watching the corn grow.

b. This a randomized block design with fields as blocks and seed types as treatments.

c. This is a randomized block design with seed types as blocks and fields as treatments.

d. This is a completely randomized design because the six seed types were randomly assigned to the four fields.

e. This is a completely randomized design with24迟谤别补迟尘别苍迟蝉鈥�6 seed types and 4 fields.

According to sleep researchers, if you are between the ages of 12and 18years old, you need 9hours of sleep to function well. A simple random sample of 28students was chosen from a large high school, and these students were asked how much sleep they got the previous night. The mean of the responses was 7.9hours with a standard deviation of 2.1hours. If we are interested in whether students at this high school are getting too little sleep, which of the following represents the appropriate null and alternative hypotheses ?

  1. H0:渭=7.9and Ha:渭<7.9
  2. H0:渭=7.9and Ha:渭鈮�7.9
  3. H0:渭=9and Ha:渭鈮�9
  4. H0:渭=9and width="69" height="24" role="math">Ha:渭<9
  5. H0:渭鈮�9andHa:渭鈮�9

Which of the following is not a property of a binomial setting?

a. Outcomes of different trials are independent.

b. The chance process consists of a fixed number of trials, n.

c. The probability of success is the same for each trial.

d. Trials are repeated until a success occurs.

e. Each trial can result in either a success or a failure.

Drive-thru or go inside? Many people think it鈥檚 faster to order at the drive-thru than to order inside at fast-food restaurants. To find out, Patrick and William used a random number generator to select10times over a 2鈥�week period to visit a local Dunkin鈥� Donuts restaurant. At each of these times, one boy ordered an iced coffee at the drive-thru and the other ordered an iced coffee at the counter inside. A coin flip determined who went inside and who went to the drive-thru. The table shows the times, in seconds, that it took for each boy to receive his iced coffee after he placed the order.

Do these data provide convincing evidence at the 伪=0.05level of a difference in the true mean service time inside and at the drive-thru for this Dunkin鈥� Donuts restaurant?

Researchers suspect that Variety A tomato plants have a different average yield than Variety B tomato plants. To find out, researchers randomly select10Variety A and10Variety B tomato plants. Then the researchers divide in half each of10small plots of land in different locations. For each plot, a coin toss determines which half of the plot gets a Variety A plant; a Variety B plant goes in the other half. After harvest, they compare the yield in pounds for the plants at each location. The10differences (Variety A 鈭� Variety B) in yield are recorded. A graph of the differences looks roughly symmetric and single-peaked with no outliers. The mean difference is x-A-B=0.343051526=0.200=20%x-A-B=0.34and the standard deviation of the differences is s A-B=0.833051526=0.200=20%=sA-B=0.83.Let 渭A-B=3051526=0.200=20%渭A鈭払 = the true mean difference (Variety A 鈭� Variety B) in yield for tomato plants of these two varieties.

A 95% confidence interval for渭A-B3051526=0.200=20%渭A-Bis given by

a. 0.34卤1.96(0.83)3051526=0.200=20%0.34卤1.96(0.83)

b.0.34卤1.96(0.8310)3051526=0.200=20%0.34卤1.96(0.8310)

c. 0.34卤1.812(0.8310)3051526=0.200=20%0.34卤1.812(0.8310)

d. 0.34卤2.262(0.83)3051526=0.200=20%0.34卤2.262(0.83)

e.0.34卤2.262(0.8310)3051526=0.200=20%0.34卤2.262(0.8310)
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Statistics

Read Explanation

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

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.