Page 284 - DMGT404 RESEARCH_METHODOLOGY

Research Methodology

Notes 5. 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?
6. In hypothesis testing, if  is the probability of committing an error of Type II. The power
of the test, 1 –  is then the probability of rejecting H when H is true or not? Why?
0 A
7. In a statistical test of hypothesis, what would happen to the rejection region if , the level
of significance, is reduced?
8. 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?
9. Can the probability of a Type II error be controlled by the sample size? Why/ why not?

10. A research biologist has carried out an experiment on a random sample of 15 experimental
plots in a field. Following the collection of data, a test of significance was conducted under
appropriate null and alternative hypotheses and the P-value was determined to be
approximately .03. What does this indicate with respect to the hypothesis testing?

11. Two samples were drawn from a recent survey, each containing 500 hamlets. In the first
sample, the mean population per hamlet was found to be 100 with a S.D. of 20, while in the
second sample the mean population was 120 with a S.D. 15. Do you find the averages of the
samples to be statistically significant?
12. A simple random sample of size 100 has a mean of 15, the population variance being 25.
Find an interval estimate of the population mean with a confidence level of (i) 99% and
(ii) 95%.

13. A population consists of five numbers 2, 3, 6, 8, 11. Consider all possible samples of size
two which can be drawn with replacement from this population. Calculate the S.E. of
sample means.

14. A certain drug is claimed to be effective in curing colds; half of them were given sugar
pills. The patients’ reactions to the treatment are recorded in the following table.
Helped Harmed No effect
Drug 52 10 18
Sugar pills 44 10 26

Test the hypothesis that the drug is no better than the sugar pills for curing colds. (The 5 %
value of x for v = 2 = 5.991)
2

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