A scale factor of 1/2 makes the triangle half the size of the original.
The original is 4 units tall, so 1/2 scale makes the new one 2 units tall.
It is 6 units long, so 1/2 would be 3 units long.
Now since the scale factor is centered at (-1,3) fine the midpoint between The top left corner of the triangle and the center point:
Midpoint ( -1-5/2 , 3+7/2)
Midpoint = (-6/2 , 10/2)
Midpoint = -3,5
This is where the top left corner of the scaled triangle would be.
See attached picture:
Answer:
a)
The null hypothesis is
The alternative hypothesis is
b-1) The value of the test statistic is t = 1.86.
b-2) The p-value is of 0.0348.
Step-by-step explanation:
Question a:
Test if the battery life is more than twice of 5 hours:
Twice of 5 hours = 5*2 = 10 hours.
At the null hypothesis, we test if the battery life is of 10 hours or less, than is:
At the alternative hypothesis, we test if the battery life is of more than 10 hours, that is:
b-1. Calculate the value of the test statistic.
The test statistic is:
We have the standard deviation for the sample, so the t-distribution is used to solve this question
In which X is the sample mean, is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.
10 is tested at the null hypothesis:
This means that
In order to test the claim, a researcher samples 45 units of the new phone and finds that the sample battery life averages 10.5 hours with a sample standard deviation of 1.8 hours.
This means that
Then
The value of the test statistic is t = 1.86.
b-2. Find the p-value.
Testing if the mean is more than a value, so a right-tailed test.
Sample of 45, so 45 - 1 = 44 degrees of freedom.
Test statistic t = 1.86.
Using a t-distribution calculator, the p-value is of 0.0348.