3x+2y=3y-2 line 1 x+y=10 line 2 solve for x/y
1 answer:
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<h2>Answer:</h2>
(a)
The probability is : 1/2
(b)
The probability is : 1/2
<h2>Step-by-step explanation:</h2>The numbers 1, 2, 3, 4, and 5 are written on slips of paper, and 2 slips are drawn at random one at a time without replacement.
The total combinations that are possible are:
(1,2) (1,3) (1,4) (1,5)
(2,1) (2,3) (2,4) (2,5)
(3,1) (3,2) (3,4) (3,5)
(4,1) (4,2) (4,3) (4,5)
(5,1) (5,2) (5,3) (5,4)
i.e. the total outcomes are : 20
(a)
Let A denote the event that the first number is 4.
and B denote the event that the sum is: 9.
Let P denote the probability of an event.
We are asked to find:
P(A|B)
We know that it could be calculated by using the formula:
Hence, based on the data we have:
( Since, out of a total of 20 outcomes there is just one outcome which comes in A∩B and it is: (4,5) )
and
( since, there are just two outcomes such that the sum is: 9
(4,5) and (5,4) )
Hence, we have:
(b)
Let A denote the event that the first number is 3.
and B denote the event that the sum is: 8.
Let P denote the probability of an event.
We are asked to find:
P(A|B)
Hence, based on the data we have:
( since, the only outcome out of 20 outcomes is: (3,5) )
and
( since, there are just two outcomes such that the sum is: 8
(3,5) and (5,3) )
Hence, we have:
Answer:
If we compare the p value obtained and the significance level given we have
so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of students reported experiencing excessive daytime sleepiness (EDS) is significantly higher than 0.5 or the half.
Step-by-step explanation:
1) Data given and notation
n=377 represent the random sample taken
X=209 represent the students reported experiencing excessive daytime sleepiness (EDS)
estimated proportion of students reported experiencing excessive daytime sleepiness (EDS)
is the value that we want to test
represent the significance level
Confidence=95% or 0.95
z would represent the statistic (variable of interest)
represent the p value (variable of interest)
2) Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that the true proportion is higher than 0.5:
Null hypothesis:
Alternative hypothesis:
When we conduct a proportion test we need to use the z statistic, and the is given by:
(1)
The One-Sample Proportion Test is used to assess whether a population proportion is significantly different from a hypothesized value
.
3) Calculate the statistic
Since we have all the info requires we can replace in formula (1) like this:
4) Statistical decision
It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.
The significance level provided . The next step would be calculate the p value for this test.
Since is a right tailed test the p value would be:
If we compare the p value obtained and the significance level given we have
so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of students reported experiencing excessive daytime sleepiness (EDS) is significantly higher than 0.5 or the half.