There are a couple of questions I still can't figure out after
the paper. I can't get Q5 part (ii) (are we supposed to use the
graph?) but I'm typing out the whole question. Q10 is simple enough
except for the 'combining the two samples' part - I'm sure it's
very logical but we've never attempted such a question before. Can
anyone help? Thank you.
Qn 5) A spot of light on a computer screen moves in a horizontal
line across the screen. At time t seconds, its distance,
x mm, from the left-hand edge of the screen is give, for
t >= 0, by
x = t^3 - 12t^2 + kt,
where k is a positive constant. Find the set of values of
k for which x is an increasing function of
t.
It is now give that k = 36.
(i) Sketch the graph of x against t.
(ii) The screen has width 375mm. Find the time in seconds at
which the spot reaches the right-hand edge of the screen, giving
your answer correct to 1 decimal place.
Qn 10) A consumer association is testing the lifetime of a
particular type of battery that is claimed to have a lifetime of
150 hours. A random sample of 70 batteries of this type is tested
and the lifetime, x hours, of each battery is measured.
The results are summarised by
Σx= 10 317, Σx^2= 1 540 231
The population mean lifetime is denoted by μ hours. The
null hypothesis μ = 150 is to be tested against the
alternative hypothesis μ < 150. Find the
p-value of the test and state the meaning of this
p-value in the context of the question.
A second random sample of 50 batteries of this type is tested
and the lifetime, y hours, of each battery is measured,
with results summarised by
Σy= 7331, Σy^2= 1 100 565
Combining the two samples into a single sample, carry out a
test, at the 10% significance level, of the same null and
alternative hypothesis.