Answer 6 for me I’m in a hurry
2 answers:
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Answer:
a) Expected value = 6.406
Variance = 4.905
Standard deviation = 2.45
b) The probability is 0.08547
Step-by-step explanation:
a) Let's suppose that:
X₁ = number of 6´s
X₂ = number of Jack, Queen, King or Aces
The mean of X₁ is:
MeanX₁ = n * p = 20 * (1/6) = 3.33
The variance of X₁ is:
The mean of X₂ is:
MeanX₂ = 10 * (16/52) = 3.076
The variance of X₂ is:
The expect value of X is:
Xexp = MeanX₁ + MeanX₂ = 3.33 + 3.076 = 6.406
The variance of X is:
VarX = VarX₁ + VarX₂ = 2.775 + 2.13 = 4.905
The standard deviation is:
Xdevi = 4.905/2 = 2.45
b) The probability of drawing at least five six out of 20 rolls is equal to:
∑(1/6)ˣ(5/6)²⁰⁻ˣ = 0.231 with x = 5
The probability of at least 4 Jack, Queen, Kings or Aces is:
∑(16/52)ˣ(1-(16/52))¹⁰⁻ˣ = 0.37 with x = 4
The probability of given event is equal to:
P = 0.231 * 0.37 = 0.08547
Answer:
Null hypothesis:
Alternative hypothesis:
Since is a left tailed test the p value would be:
So the p value obtained was a very high value and using the significance level assumed we have
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis.
Be Careful with the system of hypothesis!
If we conduct the test with the following hypothesis:
Null hypothesis:
Alternative hypothesis:
So the p value obtained was a very low value and using the significance level assumed we have
so we can conclude that we have enough evidence to reject the null hypothesis.
Step-by-step explanation:
1) Data given and notation
n=110 represent the random sample taken
X=97 represent the students who completed the modules before class
estimated proportion of students who completed the modules before class
is the value that we want to test
represent the significance level
z would represent the statistic (variable of interest)
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 assumed . The next step would be calculate the p value for this test.
Since is a left tailed test the p value would be:
So the p value obtained was a very high value and using the significance level assumed we have
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis.
Be Careful with the system of hypothesis!
If we conduct the test with the following hypothesis:
Null hypothesis:
Alternative hypothesis:
So the p value obtained was a very low value and using the significance level assumed we have
so we can conclude that we have enough evidence to reject the null hypothesis.