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12.7 Review

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This module provides a review of F Distribution and One-Way ANOVA as a part of Collaborative Statistics collection (col10522) by Barbara Illowsky and Susan Dean.

The next two questions refer to the following situation:

Suppose that the probability of a drought in any independent year is 20%. Out of those years in which a drought occurs, the probability of water rationing is 10%. However, in any year, the probability of water rationing is 5%.

What is the probability of both a drought and water rationing occurring?

0.02

Out of the years with water rationing, find the probability that there is a drought.

0.40

The next three questions refer to the following survey:

Favorite type of pie by gender
apple pumpkin pecan
female 40 10 30
male 20 30 10

Suppose that one individual is randomly chosen. Find the probability that the person’s favorite pie is apple or the person is male.

100 140 size 12{ { { size 8{"100"} } over { size 8{"140"} } } } {}

Suppose that one male is randomly chosen. Find the probability his favorite pie is pecan.

10 60 size 12{ { { size 8{"10"} } over { size 8{"60"} } } } {}

Conduct a hypothesis test to determine if favorite pie type and gender are independent.

p-value = 0 ; Reject null; Conclude dependent events

The next two questions refer to the following situation:

Let’s say that the probability that an adult watches the news at least once per week is 0.60.

We randomly survey 14 people. On average, how many people do we expect to watch the news at least once per week?

8.4

We randomly survey 14 people. Of interest is the number that watch the news at least once per week. State the distribution of X . X ~

B 14 , 0 . 60 size 12{B left ("14",0 "." "60" right )} {}

The following histogram is most likely to be a result of sampling from which distribution?

Histogram with 7 bars.

  • Chi-Square
  • Geometric
  • Uniform
  • Binomial

D

The ages of De Anza evening students is known to be normally distributed with a population mean of 40 and a population standard deviation of 6. A sample of 6 De Anza evening students reported their ages (in years) as: 28; 35; 47; 45; 30; 50. Find the probability that the mean of 6 ages of randomly chosen students is less than 35 years. Hint: Find the sample mean.

0.3669

The next three questions refer to the following situation:

The amount of money a customer spends in one trip to the supermarket is known to have an exponential distribution. Suppose the mean amount of money a customer spends in one trip to the supermarket is $72.

Find the probability that one customer spends less than $72 in one trip to the supermarket?

0.6321

Suppose 5 customers pool their money. (They are poor college students.) How much money altogether would you expect the 5 customers to spend in one trip to the supermarket (in dollars)?

$360

State the distribution to use if you want to find the probability that the mean amount spent by 5 customers in one trip to the supermarket is less than $60.

N 72 , 72 5 size 12{N left ("72", { { size 8{"72"} } over { size 8{ sqrt {5} } } } right )} {}

A math exam was given to all the fifth grade children attending Country School. Two random samples of scores were taken. The null hypothesis is that the mean math scores for boys and girls in fifth grade are the same. Conduct a hypothesis test.

n size 12{n} {} x ¯ size 12{ {overline {x}} } {} s 2 size 12{s rSup { size 8{2} } } {}
Boys 55 82 29
Girls 60 86 46

p-value = 0.0006 ; Reject null; Conclude averages are not equal

In a survey of 80 males, 55 had played an organized sport growing up. Of the 70 females surveyed, 25 had played an organized sport growing up. We are interested in whether the proportion for males is higher than the proportion for females. Conduct a hypothesis test.

p-value = 0 ; Reject null; Conclude proportion of males is higher

Which of the following is preferable when designing a hypothesis test?

  • Maximize α size 12{α} {} and minimize β size 12{β} {}
  • Minimize α size 12{α} {} and maximize β size 12{β} {}
  • Maximize α size 12{α} {} and β size 12{β} {}
  • Minimize α size 12{α} {} and β size 12{β} {}

D

The next three questions refer to the following situation:

120 people were surveyed as to their favorite beverage (non-alcoholic). The results are below.

Preferred beverage by age
0 – 9 10 – 19 20 – 29 30 + Totals
Milk 14 10 6 0 30
Soda 3 8 26 15 52
Juice 7 12 12 7 38
Totals 24 30 44 22 120

Are the events of milk and 30+ :

  • Independent events? Justify your answer.
  • Mutually exclusive events? Justify your answer.
  • No
  • Yes, P M and 30 + = 0 size 12{P left ( ital "Mand""30"+{} right )=0} {}

Suppose that one person is randomly chosen. Find the probability that person is 10 – 19 given that he/she prefers juice .

12 38 size 12{ { { size 8{"12"} } over { size 8{"38"} } } } {}

Are Preferred Beverage and Age independent events? Conduct a hypothesis test.

No; p-value = 0

Given the following histogram, which distribution is the data most likely to come from?

Histogram with 8 bars.

  • uniform
  • exponential
  • normal
  • chi-square

A

Questions & Answers

what is biology
Hajah Reply
the study of living organisms and their interactions with one another and their environments
AI-Robot
what is biology
Victoria Reply
HOW CAN MAN ORGAN FUNCTION
Alfred Reply
the diagram of the digestive system
Assiatu Reply
allimentary cannel
Ogenrwot
How does twins formed
William Reply
They formed in two ways first when one sperm and one egg are splited by mitosis or two sperm and two eggs join together
Oluwatobi
what is genetics
Josephine Reply
Genetics is the study of heredity
Misack
how does twins formed?
Misack
What is manual
Hassan Reply
discuss biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles
Joseph Reply
what is biology
Yousuf Reply
the study of living organisms and their interactions with one another and their environment.
Wine
discuss the biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles in an essay form
Joseph Reply
what is the blood cells
Shaker Reply
list any five characteristics of the blood cells
Shaker
lack electricity and its more savely than electronic microscope because its naturally by using of light
Abdullahi Reply
advantage of electronic microscope is easily and clearly while disadvantage is dangerous because its electronic. advantage of light microscope is savely and naturally by sun while disadvantage is not easily,means its not sharp and not clear
Abdullahi
cell theory state that every organisms composed of one or more cell,cell is the basic unit of life
Abdullahi
is like gone fail us
DENG
cells is the basic structure and functions of all living things
Ramadan
What is classification
ISCONT Reply
is organisms that are similar into groups called tara
Yamosa
in what situation (s) would be the use of a scanning electron microscope be ideal and why?
Kenna Reply
A scanning electron microscope (SEM) is ideal for situations requiring high-resolution imaging of surfaces. It is commonly used in materials science, biology, and geology to examine the topography and composition of samples at a nanoscale level. SEM is particularly useful for studying fine details,
Hilary
cell is the building block of life.
Condoleezza Reply
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Source:  OpenStax, Collaborative statistics for mt230. OpenStax CNX. Aug 18, 2011 Download for free at http://legacy.cnx.org/content/col11345/1.2
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