Answer:
3. t-test for the difference between means for two related samples.
Step-by-step explanation:
It is given that a professor of UCI wishes to study what really the students remember from their elementary school days and other such stuffs that were very popular at that time.
therefore the professor put forward two test. In one of the test, he put some question from the elementary school and in other he put one question about a pop culture from that time. He used the same sample for both the tests.
So, since the professor involved the same set of students in his experiment for both the tests, so both the samples are related samples.
Therefore, the test uses is a t - test that is used for the difference between the related samples.
Answer:
The equation of line having slope m and y-intercept b is
y = m x + b
The other two equations of line in the same family having intercepts p and q are,keeping the slope same i.e m , described in the question are
→ y= m x + p
→ y = m x + q
As both the equation have same slope i.e m , so lines will be parallel, but their Y - intercept are different i.e distance from the origin where it cuts the y-axis are different i.e at a distance of p and q from origin.
= 98 2/3
= 98 + 2/3
= 98/1 + 2/3
= (98/1 * 3/3) + 2/3
= 294/3 + 2/3
= 296/3
= 296 ÷ 3
= 98.666667
Given that mean=3750 hours and standard deviation is 300:
Then:
<span>a. The probability that a lamp will last for more than 4,000 hours?
P(x>4000)=1-P(x<4000)
but
P(x<4000)=P(z<Z)
where:
z=(x-</span>μ)/σ
z=(4000-3750)/300
z=0.833333
thus
P(x<4000)=P(z<0.8333)=0.7967
thus
P(x>4000)=1-0.7967=0.2033
<span>b.What is the probability that a lamp will last less than 3,000 hours?
P(x<3000)=P(z<Z)
Z=(3000-3750)/300
z=-2.5
thus
P(x<3000)=P(z<-2.5)=0.0062
c. </span><span>.What lifetime should the manufacturer advertise for these lamps in order that only 4% of the lamps will burn out before the advertised lifetime?
the life time will be found as follows:
let the value be x
the value of z corresponding to 0.04 is z=-2.65
thus
using the formula for z-score:
-2.65=(x-3750)/300
solving for x we get:
-750=x-3750
x=-750+3750
x=3000</span>
