Math 1030 Quiz 1
Mark
/ 5
You will have 30 minutes to answer these questions.
Questions must be answered in the order given and you should show all your working
including the final answer.
Question 1: [2.5 Mark]
The Lecturer of Math 1030 believes students sleep less than 7 hours per night
In a sample of randomly selected 11 students, it was found that the sample mean hours sleep was 6.182 and the sample standard
deviation is 2.1826.
Using 5 % level of significance, test the hypothesis that students sleep less than 7 hour per night.
You can suppose the hours sleep is normally distributed.
Include all the steps for Hypothesis testing
1) H0 = u = 7
Ha = u = <7
2) Since o is given z = (x-u)/(o/sqrt(n))
3) A = 0.05
z = -1.645
4) Reject Ho if |u| > 1.645
5) Z = 6.182-7/(2.1826/(sqrt 11))
= -1.24
6) Since -1.24 is less than |u|>1.645, we cannot reject Ho
We cannot conclude that students sleep less than 7 hours a night
Question 2: [ 2.5 Mark]
Leading up to each federal election, the various opinion pollsters conduct nation-wide surveys of electors in an
attempt to forecast the proportion of the electorate who will vote for each of the major parties.
Suppose that a polling firm conducts a survey of 500 randomly selected electors (a representative sample), and
their results indicate that 210 of these electors will vote for the ALP at the election.
Test the hypothesis at 10 % level of significance that the proportion for those who will vote for the APL at the
election is different to 50%
Include all the steps for Hypothesis testing
1) Ho: p = 0.5
Ha: p =/= 0.5
2) Since n is large:
z = P^-P/sqrt (pq/n)
3) A = 0.05 (1-(a/2), z = 1.645
4) Reject Ho if |z| > 1.645
5) p^- = x/n = 210/500 = 0.42
z = 0.42-0.5/((sqrt(0.5x0.5)/500))
z = -3.577
6)
since -3.577 is less than 1.645, we cannot reject Ho
We cannot conclude that the proportion of those who will vote for the APL at the election is
different to 50%