Research Methodology - Dr. Krishan K. Pandey

232 Research Methodology
28. (i) A random sample from 200 villages was taken from Kanpur district and the average population per
village was found to be 420 with a standard deviation of 50. Another random sample of 200 villages from
the same district gave an average population of 480 per village with a standard deviation of 60. Is the
difference between the averages of the two samples statistically significant? Take 1% level of significance.
(ii) The means of the random samples of sizes 9 and 7 are 196.42 and 198.42 respectively. The sums of he
squares of the deviations from the mean are 26.94 and 18.73 respectively. Can the samples be constituted
to have been drawn from the same normal population? Use 5% level of significance.
29. A farmer grows crops on two fields A and B. On A he puts Rs. 10 worth of manure per acre and on B Rs 20
worth. The net returns per acre exclusive of the cost of manure on the two fields in the five years are:
Year 1 2 3 4 5
Field A, Rs per acre 34 28 42 37 44
Field B, Rs per acre 36 33 48 38 50
Other things being equal, discuss the question whether it is likely to pay the farmer to continue the more
expensive dressing. Test at 5% level of significance.
30. ABC Company is considering a site for locating their another plant. The company insists that any
location they choose must have an average auto traffic of more than 2000 trucks per day passing the site.
They take a traffic sample of 20 days and find an average volume per day of 2140 with standard deviation
equal to 100 trucks.
Answer the following:
(i) If α = .05, should they purchase the site?
(ii) If we assume the population mean to be 2140, what is the β error?