/*! 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} Q39 Using Probability to Form Conclu... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Q39 (page 146)

Using Probability to Form Conclusions. In Exercises 37鈥�40, use the given probability value to determine whether the sample results could easily occur by chance, then form a conclusion.

Coffee Talk A study on the enhancing effect of coffee on long-term memory found that 35 participants given 200 mg of caffeine performed better on a memory test 24 hours later compared to the placebo group that received no caffeine.

a. There was a probability of 0.049 that the difference between the coffee group and the placebo group was due to chance. What do you conclude?

b. A group given a higher dose of 300 mg performed better than the 200 mg group, with a probability of 0.75 that this difference is due to chance. What do you conclude?

Short Answer

Expert verified

(a)

The difference between the 200 mg coffee group and the placebo does not occur by chance. It can be concluded that a dose of 200 mg has a significant effect on memory.

(b)

The 300 mg coffee group performed better than the 200 mg coffee group by chance.

Thus, the dose of 300 mg coffee does not have a significantly better effect on memory than a dose of 200 mg coffee.

Step by step solution

01

Given information

The group with no caffeine did not perform better on a memory test than the group of 35 participants that took 200 mg of caffeine.

The group given a dose of 300 mg performed better than a group given 200 mg, displaying a probability of 0.75 by chance.

02

Probability analysis

Theprobability value is the value between 0 and 1 that gives an idea of the degree of possibility of occurrence of an event. A value lower than 0.05 would imply that the event is unusual or unlikely to occur.

03

Interpret the probability value to establish the difference between two groups

(a)

It is known that the probability of getting the difference between the memory test for two groups by chance is 0.049.

The probability that the difference between memory test results for the 200 mg coffee group and the placebo group has occurred due to chance is 0.049.

This is lower than 0.05. Thus, it can be said that the difference has not occurred by chance.

Therefore, it can be concluded that a dose of 200 mg coffee has a significant effect on memory.

04

Interpret the probability for the difference between two groups 

(b)

It is required to evaluate the difference in memory test results for two groups:

  • 300 mg dose of caffeine
  • 200 mg dose of caffeine

The probability that the 300 mg dose performed better by chance is 0.75.

The probability that the difference between the 300 mg coffee group and the 200mg group on memory has occurred due to chance is equal to 0.75.

The value is greater than 0.05.

Thus, it can be said that the 300 mg dose group performed better than the 200 mg dose group by chance.

Therefore, it can be concluded that a dose of 300 mg coffee does not have a significantly better effect on memory than a dose of 200mg coffee.

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

Redundancy in Computer Hard Drives Assume that there is a 3% rate of disk drive failures in a year (based on data from various sources including lifehacker.com).

a. If all of your computer data is stored on a hard disk drive with a copy stored on a second hard disk drive, what is the probability that during a year, you can avoid catastrophe with at least one working drive? Express the result with four decimal places.

b. If copies of all of your computer data are stored on three independent hard disk drives, what is the probability that during a year, you can avoid catastrophe with at least one working drive? Express the result with six decimal places. What is wrong with using the usual round-off rule for probabilities in this case?

In Exercises 9鈥�20, use the data in the following table, which lists drive-thru order accuracy at popular fast food chains (data from a QSR Drive-Thru Study). Assume that orders are randomly selected from those included in the table.

惭肠顿辞苍补濒诲鈥檚

Burger King

奥别苍诲测鈥檚

Taco Bell

Order Accurate

329

264

249

145

OrderNotAccurate

33

54

31

13

Fast Food Drive-Thru Accuracy If two orders are selected, find the probability that they are both from Taco Bell.

a. Assume that the selections are made with replacement. Are the events independent?

b. Assume that the selections are made without replacement. Are the events independent?

In Exercises 29 and 30, find the probabilities and indicate when the 鈥�5% guideline for cumbersome calculations鈥� is used.

Medical Helicopters In a study of helicopter usage and patient survival, results were obtained from 47,637 patients transported by helicopter and 111,874 patients transported by ground (based on data from 鈥淎ssociation Between Helicopter vs Ground Emergency Medical Services and Survival for Adults with Major Trauma,鈥� by Galvagno et al., Journal of the American Medical Association, Vol. 307, No. 15).

a. If 1 of the 159,511 patients in the study is randomly selected, what is the probability that the subject was transported by helicopter?

b. If 5 of the subjects in the study are randomly selected without replacement, what is the probability that all of them were transported by helicopter

Language: Complement of 鈥淎t Least One鈥� Let A = the event of getting at least one defective iPhone when 3 iPhones are randomly selected with replacement from a batch. Write a statement describing eventA炉.

In Exercises 25鈥�32, find the probability and answer the questions.

X-Linked Genetic Disease Men have XY (or YX) chromosomes and women have XX chromosomes. X-linked recessive genetic diseases (such as juvenile retinoschisis) occur when there is a defective X chromosome that occurs without a paired X chromosome that is not defective. In the following, represent a defective X chromosome with lowercase x, so a child with the xY or Yx pair of chromosomes will have the disease and a child with XX or XY or YX or xX or Xx will not have the disease. Each parent contributes one of the chromosomes to the child.

a. If a father has the defective x chromosome and the mother has good XX chromosomes, what is the probability that a son will inherit the disease?

b. If a father has the defective x chromosome and the mother has good XX chromosomes, what is the probability that a daughter will inherit the disease? c. If a mother has one defective x chromosome and one good X chromosome and the father has good XY chromosomes, what is the probability that a son will inherit the disease?

d. If a mother has one defective x chromosome and one good X chromosome and the father has good XY chromosomes, what is the probability that a daughter will inherit the disease?
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Calculus

Read Explanation

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics 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.