Approximately 86.5% of Americans commute to work by car, truck, or van. Out of that group, 84.6% drive alone and 15.4% drive in a carpool. Approximately 3.9% walk to work and approximately 5.3% take public transportation.
Construct a table or a tree diagram of the situation. Include a branch for all other modes of transportation to work.
Assuming that the walkers walk alone, what percent of all commuters travel alone to work?
Suppose that 1,000 workers are randomly selected. How many would you expect to travel alone to work?
Suppose that 1,000 workers are randomly selected. How many would you expect to drive in a carpool?
Car, Truck or Van
Walk
Public Transportation
Other
Totals
Alone
0.7318
Not Alone
0.1332
Totals
0.8650
0.0390
0.0530
0.0430
1
If we assume that all walkers are alone and that none from the other two groups travel alone (which is a big assumption) we have:
P (Alone) = 0.7318 + 0.0390 = 0.7708.
Make the same assumptions as in (b) we have: (0.7708)(1,000) = 771
When the Euro coin was introduced in 2002, two math professors had their statistics students test whether the Belgian one Euro coin was a fair coin. They spun the coin rather than tossing it and found that out of 250 spins, 140 showed a head (event
H ) while 110 showed a tail (event
T ). On that basis, they claimed that it is not a fair coin.
Based on the given data, find
P (
H ) and
P (
T ).
Use a tree to find the probabilities of each possible outcome for the experiment of tossing the coin twice.
Use the tree to find the probability of obtaining exactly one head in two tosses of the coin.
Use the tree to find the probability of obtaining at least one head.
Use the following information to answer the next two exercises. The following are real data from Santa Clara County, CA. As of a certain time, there had been a total of 3,059 documented cases of AIDS in the county. They were grouped into the following categories:
* includes homosexual/bisexual IV drug users
Homosexual/Bisexual
IV Drug User*
Heterosexual Contact
Other
Totals
Female
0
70
136
49
____
Male
2,146
463
60
135
____
Totals
____
____
____
____
____
Suppose a person with AIDS in Santa Clara County is randomly selected.
Find
P (Person is female).
Find
P (Person has a risk factor heterosexual contact).
Find
P (Person is female OR has a risk factor of IV drug user).
Find
P (Person is female AND has a risk factor of homosexual/bisexual).
Find
P (Person is male AND has a risk factor of IV drug user).
Find
P (Person is female GIVEN person got the disease from heterosexual contact).
Construct a Venn diagram. Make one group females and the other group heterosexual contact.
Answer these questions using probability rules. Do NOT use the contingency table. Three thousand fifty-nine cases of AIDS had been reported in Santa Clara County, CA, through a certain date. Those cases will be our population. Of those cases, 6.4% obtained the disease through heterosexual contact and 7.4% are female. Out of the females with the disease, 53.3% got the disease from heterosexual contact.
Find
P (Person is female).
Find
P (Person obtained the disease through heterosexual contact).
Find
P (Person is female GIVEN person got the disease from heterosexual contact)
Construct a Venn diagram representing this situation. Make one group females and the other group heterosexual contact. Fill in all values as probabilities.
A hypothesis in a scientific context, is a testable statement about the relationship between two or more variables or a proposed explanation for some observed phenomenon. In a scientific experiment or study, the hypothesis is a brief summation of the researcher's prediction of the study's findings.
Hamzah
Which may be supported or not by the outcome. Hypothesis testing is the core of the scientific method.
Hamzah
statistics means interpretation analysis and representation of numerical data
Ramzan
To check the statment or assumption about population parameter is xalled hypothesis
Ali
hypothesis is simply an assumption
Patrick
what is the d.f we know that how to find but basically my question is what is the d.f? any concept please
Degrees of freedom aren’t easy to explain. They come up in many different contexts in statistics—some advanced and complicated. In mathematics, they're technically defined as the dimension of the domain of a random vector.
Hamzah
d.f >> Degrees of freedom aren’t easy to explain. They come up in many different contexts in statistics—some advanced and complicated. In mathematics, they're technically defined as the dimension of the domain of a random vector.
Hamzah
But we won't get into that. Because degrees of freedom are generally not something you needto understand to perform a statistical analysis—unless you’re a research statistician, or someone studying statistical theory.
Hamzah
And yet, enquiring minds want to know. So for the adventurous and the curious, here are some examples that provide a basic gist of their meaning in statistics.
Hamzah
The Freedom to Vary
First, forget about statistics. Imagine you’re a fun-loving person who loves to wear hats. You couldn't care less what a degree of freedom is. You believe that variety is the spice of life
Unfortunately, you have constraints. You have only 7 hats. Yet you want to wear a different
Hamzah
hat every day of the week.
On the first day, you can wear any of the 7 hats. On the second day, you can choose from the 6 remaining hats, on day 3 you can choose from 5 hats, and so on.
Hamzah
When day 6 rolls around, you still have a choice between 2 hats that you haven’t worn yet that week. But after you choose your hat for day 6, you have no choice for the hat that you wear on Day 7. You must wear the one remaining hat. You had 7-1 = 6 days of “hat” freedom—in which the hat you wore
Hamzah
That’s kind of the idea behind degrees of freedom in statistics. Degrees of freedom are often broadly defined as the number of "observations" (pieces of information) in the data that are free to vary when estimating statistical parameters.
binomial distribution and poisson both are used to estimate the number of successes probable against the. probable failures.
the difference is only that BINOMIAL dist. is for discrete data while POISSON is used for continuous data.
Salman
What do you need to understand?
Angela
The binomial distribution is frequently used to model the number of successes in a sample of size n drawn with replacement from a population of size N. If the sampling is carried out without replacement, the draws are not independent and so the resulting distribution is a hypergeometric distribution
Hamzah
poisson distribution is also for discrete data set. The difference is when the probability of occurring an event is very little and the sample size is extra large then we use poisson distribution.
Neil
Neil
yes you got it and very interested answer you gave
1 tail if greater than pr less than.2 tail if not equal.
Jojo
in such a case there is no sufficient information provided to develop an alternative hypothesis and we can decide between only two states i.e either the statement is EQUAL TO or NOT EQUAL TO under given conditions
Salman
for 1tail there must be certain criteria like the greater than or less than or some probability value that must be achieved to accept or reject the original hypothesis.
Salman
for example if we have null hypothesis
Ho:u=25
Ha:u#25(not equal to 25) it would be two tail
if we say
Ho:u=25
Ha:u>or
Ha:u<25 it would be consider as one tail
I hope you will be understand
#Coleen
Shabir
yes its true. now you have another problem. so share.
Different data sets will have different means and standard deviations, so values from one set cannot always be compared directly with those from another. The z-score standardizes normally distributed data sets, allowing for a proper comparison and a consistent definition of percentiles across data s
summation of values of x1 x2 x3 ,,,,xn divided by total number n
if it is with frequency its like this
summation of values of x1f1+x2f2+x3f3+xnfk divided by summation of frequencies like f1+f2+f3+fk
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