Page 439 - DMTH404_STATISTICS

Unit 31: Hypothesis Testing

31.7 Self Assessment Notes

1. Fill in the blanks:

(i) The reciprocal of standard error of an estimator is ...... .
(ii) ...... tailed test is used when H is  ³ or £  .
0 0
(iii) For testing H :  =  or  =  (s known), we always use ...... normal test.
0 0 1 2
(iv) When s = s = s is not known, we compute its ...... estimate from sample.
1 2
(v) The  - test is used to test H : s = s only in case of a ...... sample.
2
0 0
(vi) The test of hypothesis regarding equality of standard deviations makes use of ......
statistics.
(vii) The test of goodness of fit or of independence is always a ...... tailed test.

(viii) When sample (from normal population) sizes are small and s and s are not known,
1 2
the sampling distribution of the difference of sample means follows t - distribution
under the assumption that ...... .
(ix) The existence of a strong linear relationship between two variables implies that the
regression coefficient is ...... .
(x) Yate's correction for continuity is needed when sample size is ...... .

31.8 Review Questions

1. Certain motor oil is packed in tins holding 5 litres each. The filling machine can maintain
this but with a S.D. of 0.15 litre. Two samples of 36 tins each are taken from the production
line. If the sample means are 5.20 and 4.95 litres respectively, can we be 99% sure that the
sample have come from a population of 5 liters?
.
2 58 015
´
.
Hint : Check whether the two sample means lie in the interval 5± or not.
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2. The Industrial Placement Unit of Unisex Polytechnic believes that the average salary paid
to the students during their industrial year is Rs 2,800. A sample of 17 of its own students
reveals that their average salary is Rs 2,860 with a S.D. of Rs 105. Does this evidence
suggest that the countrywide average salary is higher than Rs 2,800? Let the level of
significance be 5%.
Hint : Use one tailed test.
4. In a survey of buying habits, 400 women shoppers are chosen at random in super market
A located in a certain section of the city. Their average weekly food expenditure is Rs 250
with a S.D. of Rs 40. For 400 women shoppers chosen at random in super market B in
another section of the city, the average weekly food expenditure is Rs 220 with a S.D. of
Rs 55. Test at 1% level of significance whether the average weekly food expenditure of the
population of shoppers are equal?
Hint : Apply two tailed test to test the hypothesis regarding equality of means. Also note
that both the samples are large.

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