ECON1320 CML

Q1 The four major competitors in the computer work-station market are Sun Microsystems (29%), Hewlett-Packard (18.8%), IBM (16%),and Digital Equipment (11.6%) with other manufacturers holding 24.6% of the market. One year later a survey of computer workstations found 97 Sun, 86 HP, 70 IBM, 60 Digital and 82 other. Test at the 2.5% level of significance whether changes have occurred during the 1-year period.

1. State the critical value for the test.
2. Find the value of the test statistic (to 3 dec pl).
3. Can we conclude that the proportions have changed during the year? (yes/no)
OBSERVED
EXPECTED
(o-e)^2/e
97
115.42
2.939667
86
74.824
1.66929
73
63.68
1.364045
60
46.168
4.144087
82
97.908
2.584717
398
chi square value
12.70181

Critical value = 12.8
Test value = 12.701
No proportions have not changed.
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Q2
A film director wished to determine whether there existed a relationship between movie success and whether or not the movie was in 2D, 3D or Black and White.

Very unsuccessful Low success Medium success High success
2D 24 53 75 83
3D 29 56 93 109
Black and White 16 32 86 113

Assume that a 2.5% level of significance is to be used for the test.

1. Calculate the test statistic, reporting your answer correct to three decimal places.
Use the tables to determine the lower and upper bounds on the p-value for the test.

2. lower bound (if the lower bound is outside the values of the tables, type lt in the box)
3. upper bound (if the upper bound is outside the values of the tables, type gt in the box)

4. Is the null hypothesis rejected for this test? Type yes or no.
5. Hence, on the basis of this test, is there a relationship between movie success and whether or not the movie is in 2D, 3D or Black and White? Type yes or no.
Ho: type of movie and its success are independent
H1: type of movie and its success are not independent

OBSERVED
EXPECTED