Page 258 - DMGT209_QUANTITATIVE_TECHNIQUES_II

Unit 13: Test of Significance

Significance Level: Significance level is the criterion used for rejecting the null hypothesis. Notes

Tests for statistical significance: Tests for statistical significance are used to estimate the
probability that a relationship observed in the data occurred only by chance; the probability
that the variables are really unrelated in the population.

13.5 Review Questions

1. Each person in a random sample of 50 was asked to state his/her sex and preferred colour.
The resulting frequencies are shown below.
Red Blue Green
Colour
Male 5 14 6
Sex Female 15 6 4

A chi-square test is used to test the null hypothesis that sex and preferred colour are
independent. Will you reject at the null hypothesis 0.005 level? Why/ Why not?
2. Are all employees equally prone to having accidents? To investigate this hypothesis,
Parry (1985) looked at a light manufacturing plant and classified the accidents by type and
by age of the employee.

Accident Type
Age
Sprain Burn Cut
Under 25 9 17 5
25 or over 61 13 12

A chi-square test gave a test-statistic of 20.78. If we test at a =.05, does the proportion of
sprain, cuts and burns seems to be similar for both age classes? Why/ why not?

3. In hypothesis testing, if is the probability of committing an error of Type II. The power of
the test, is then the probability of rejecting H0 when HA is true or not? Why?
4. In a statistical test of hypothesis, what would happen to the rejection region if , the level of
significance, is reduced?
5. During the pre-flight check, Pilot Mohan discovers a minor problem - a warning light
indicates that the fuel gauge may be broken. If Mohan decides to check the fuel level by
hand, it will delay the flight by 45 minutes. If he decides to ignore the warning, the aircraft
may run out of fuel before it gets to Mumbai. In this situation, what would be:
(a) the appropriate null hypothesis? and;
(b) a type I error?

Answers: Self Assessment

1. Large Sample Test
2. Chi-square

3. Quantitative
4. 2

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