Answer:
See the attached figure which represents the problem.
As shown, AA₁ and BB₁ are the altitudes in acute △ABC.
△AA₁C is a right triangle at A₁
So, Cos x = adjacent/hypotenuse = A₁C/AC ⇒(1)
△BB₁C is a right triangle at B₁
So, Cos x = adjacent/hypotenuse = B₁C/BC ⇒(2)
From (1) and (2)
∴ A₁C/AC = B₁C/BC
using scissors method
∴ A₁C · BC = B₁C · AC
420 inches and 35 feet
length of trim required = 84 × 5 = 420 inches
using 12 inches = 1 foot then
= 35 feet
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.