Answer:
Step-by-step explanation:
To solve this, all we need to do is draw a triangle.
From the we can deduce that
From that, we can draw our triangle as we know that tan(x) is the opposite side over the adjacent side. Attached is that triangle. Through the Pythagorean Theorem, we can find that the hypotenuse of this right triangle is
Now all we need to do is take the sin of this triangle, which is the opposite side over the hypotenuse
This gives us the value of which is our answer.
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 .