INTRODUCTORY STATISTICS Assessment: Problem Set
Q1) All first year students at the University of Irie are required to read a Foundation Course in Communications. For the purposes of Lectures, the first year intake of students are organized into two groups viz. Group A and Group B. Group B comprises students who have either an 'A' Level Pass or a Grade 'A' Pass at CXC General in English. All other students are assigned to Group A. However, both groups write the same final examination in the course.
The scores obtained in the course by two random samples of students, one from Group A and the other from Group B, are processed using MINITAB and some preliminary results are shown in Exhibit I below:
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Exhibit I
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|
Variable
|
N
|
Mean
|
Median
|
TrMean
|
StDev
|
SE mean
|
|
Group A
|
135
|
51.44
|
51.00
|
51.40
|
09.37
|
*
|
|
Group B
|
108
|
51.80
|
53.00
|
52.05
|
**
|
1.168
|
(a) Examine the results shown in Exhibit I and
(i) Fill in the gap marked * and **
(ii) Estimate the proportion of students scoring less than 60 in Group A.
(iii) Estimate the highest mark made by the first 75% of students in Group A.
(b) Exhibit II below shows the results of further analysis carried out on the Group B scores.
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Exhibit II
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|
Test of mu = 60 vs mu not = 60
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|
Variable
|
N
|
Mean
|
StDev
|
SE Mean
|
T
|
P
|
|
Group B
|
135
|
51.444
|
9.368
|
0.806
|
*
|
**
|
|
95.0% CI = (49.850, 53.039)
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(i) State the null and the alternative hypotheses for this test.
(ii) Calculate the missing value * and use tables to approximate the value of **.
(iii) If you were the statistician, what would you conclude and why?
Q2) It is claimed that the mean cost of a hotel room in Tobago is $125 US per day. A recent sample of 35 hotels showed that the mean cost of a hotel room is $138 US per day with a standard deviation of $26 US. Test at the 3% significant level if the current mean cost of a hotel room in Tobago is higher than $125US per day.