F Distribution and ANOVA: Review1.52008/06/18 09:22:33 GMT-52008/08/15 13:43:28.590 GMT-5BarbaraIllowskyillowskybarbara@deanza.eduSusanDeandeansusan@deanza.eduConnexionscnx@cnx.orgelementarystatisticsThis module provides a review of F Distribution and 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.
0.40The next three questions refer to the following survey:
Favorite Type of Pie by Genderapplepumpkinpecanfemale401030male203010
Suppose that one individual is randomly chosen. Find the probability that the person’s favorite pie is apple or the person is male.
100140 size 12{ { { size 8{"100"} } over { size 8{"140"} } } } {}
Suppose that one male is randomly chosen. Find the probability his favorite pie is pecan.
1060 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?
8.4We randomly survey 14 people. Of interest is the number that watch the news at least once per week. State the distribution of
X. X ~
B14,0.60 size 12{B left ("14",0 "." "60" right )} {}
The following histogram is most likely to be a result of sampling from which distribution?
AChi-SquareBGeometricCUniformDBinomialD
The ages of De Anza evening students is known to be normally distributed. 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 average of 6 ages of randomly chosen students is less than 35 years.
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 average 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 is if you want to find the probability that the average amount spent by 5 customers in one trip to the supermarket is less than $60.
N72,725 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 average math scores for boys and girls in fifth grade are the same. Conduct a hypothesis test.
p-value=0.0003; 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?
AMaximize
α size 12{α} {} and minimize
β size 12{β} {}BMinimize
α size 12{α} {} and maximize
β size 12{β} {}CMaximize
α size 12{α} {} and
β size 12{β} {}DMinimize
α size 12{α} {} and
β size 12{β} {}DThe next three questions refer to the following situation:120 people were surveyed as to their favorite beverage (non-alcoholic). The results are below.
Are the events of milk and 30+:
aIndependent events? Justify your answer.bMutually exclusive events? Justify your answer.aNobYes,
PMand30+=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.
1238 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?
AuniformBexponentialCnormalDchi-squareA