# ECON1320 CML

**Topics:**Statistical hypothesis testing, Inequality, Null hypothesis

**Pages:**6 (1309 words)

**Published:**September 17, 2014

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

(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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