ECON1320 CML

Topics: Statistical hypothesis testing, Inequality, Null hypothesis Pages: 6 (1309 words) Published: September 17, 2014
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.
-------------------------------------------------------
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
(o-e)^2/e
24
18.029909
1.97682567
53
43.0884265
2.27994607
75
77.6202861
0.08845496
83
93.2054616
1.11743932
29
25.7516255
0.40975809
56
52.6228869
0.21672876
93
94.7958388
0.03402087
109
113.829649
0.20491593
16
22.1625488
1.71356678
32
45.2886866
3.89918995
86
81.5838752
0.23904428
113
97.9648895
2.30750578
 
CHI SQUARE VALUE
14.4873965
1.Test statistic = 14.487
2 and 3. please provide exact tables for this part, as online table can calculate p values for any given value. 4.. Is the null hypothesis rejected for this test? NO The critical value with (4-1)*(3-1) = 6 degrees and 2.5% level is 16.3. Clearly we accept the null hypothesis 5. Movie success and type of movie ( 2D, 3D or Black and White) are independent. --------------------------------------------------------

Q3
General Motors wished to determine if its prototype diesel engine was popular between two different age groups. In a sample of 904 survey participants from the 18-35 year old age group (A), 574 indicated they approved. Meanwhile, 511 of 911 individuals surveyed from the 36+ age group (B) indicated they approved. Construct an 88% confidence interval for the difference between the proportions. Use 'A' minus 'B' and state only the upper limit correct to 3 decimal places Answer 

Upper limit = 0.038
------------------------------------------------------------------- Q4
The Australian Banking Association conducts a survey every five years into the status of women in the banking industry, including aspects relating to working hours. In the 1997 survey, which incorporated 735 respondents, 217 reported working more than 50 hours per week. Of the 583 respondents to the 2002 survey, 238 reported to be working in excess of 50 hours per week. The Australian Bankers Association is interested if there has been any change in work patterns and wished to test this proposition at the1% level of significance.

1. If the hypotheses are written in the form of the...
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