10 2/5 x 15 5/6 and 1 1/3 x 1 1/3
1 answer:
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Answer:
Null hypothesis:
Alternative hypothesis:
(1)
Since the p value obtained was a very low value and using 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 1% of significance the proportion of adults prefer window seats when they fly is significantly higher than 0.5 .
Step-by-step explanation:
1) Data given and notation
n=778 represent the random sample taken
X=492 represent the people that chose a window seat.
estimated proportion of people that chose a window seat.
is the value that we want to test
represent the significance level
Confidence=99% or 0.99
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 majority of adults prefer window seats when they fly:
Null hypothesis:
Alternative hypothesis:
When we conduct a proportion test we need to use the z statisitc, 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:
5) Conclusion
Since the p value obtained was a very low value and using 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 1% of significance the proportion of adults prefer window seats when they fly is significantly higher than 0.5 .
So have the sequence: 
To check if the sequence is geometric, we are going to find its common ratio; to do it we are going to use the formula:
where
is the common ratio
is the current term in the sequence
is the previous term in the sequence
In other words we are going to divide the current term by the previous term a few times, and we will to check if that ratio is the same:
For
and 
:
For
and 
:
For
and 
:
As you can see, we have a common ratio!
We can conclude that our sequence is a geometric sequence and its common ratio is
To check if the sequence is geometric, we are going to find its common ratio; to do it we are going to use the formula:
where
In other words we are going to divide the current term by the previous term a few times, and we will to check if that ratio is the same:
For
For
For
As you can see, we have a common ratio!
We can conclude that our sequence is a geometric sequence and its common ratio is