32. The following table presents data on the value of a harvested crop stored in the open and inside a godown:

Sample Size Mean (X - X)²

Outside 40 117 8,685

Inside 100 132 27,315 [Use =0.05]

Assuming that the two samples are random and have been obtained from nonnal populations with equal variance" examine whether the mean value of the harvested crop is affected by the weather conditions.

33. A machine produced 20 defective articles in a batch of 400. After over hauling, it produced 10 defectives articles in batch of 300. Has the machine improved after the over haul? (Take = 0.01).

34. A random sample of 200 items from a large lot contained 5 defective items. Assuming that a lot consisting of 2% or less defectives is considered as satisfactory, what are your conclusions about the lot at 5% level of significance? Clearly specify the null and the alternative hypothesis.

35. A random sample of 100 villages in a district gives the mean population of 500 persons per village. Another sample of 150 villages from the same district gives the mean of 504. If the standard deviation of the population of villages in the district is 20, find out if the mean of the first sample is significantly different from the combined mean of the two samples ? [Use =0.0]

36. A manufacturer claims that at least 90% of the machine parts that It supplied to a factory conformed to specifications. An examination of 200 such parts revealed that 160 parts were not faulty. Determine if the manufacturer's claim is legitimate at 1% level of significance?

37. Before an increase in excise duty on cigarettes, 132 persons out of a sample of 300 persons were found to be smokers. After an increase in the excise duty,156 out of a sample of 400 were found to be smokers. Is it possible to conclude, at 5% level of significance, that the increase in excise duty had an adverse effect on the habit of smoking?

38. The standard deviation of a random sample of 50 observations was calculated to be 5.5. Test the hypothesis that the standard deviation in population is 7. What would be your assumption about the nature of the population? [Use 5% level of significance.]

39. An auto company decided to introduce a new six cylinder car whose mean petrol consumption is claimed to be lower than that of the existing auto engine. It was found that the mean petrol consumption for the 50 cars was 10 km per litre with a standard deviation of 3.5 km per litre. Test for the company at 5% level of significance, whether the claim that the new car petrol consumption is 9.5 km per litre on the average is acceptable.

40. The mean lifetime of 100 fluorescent light bulbs produced by a company is computed to be 1570 hours with a standard deviation of 120 hours. If f.1is the mean lifetime of all the bulbs produced by the company, test the hypothesis =1600 hours against the alternative hypothesis = 1600 hours using a level of significance of 1%.

41. A man buys 50 electric bulbs of 'Philips' and 50 electric bulbs of 'HMT'. He finds that 'Philips' bulbs give an average life of 1500 hours with a standard deviation of 60 hours and 'HMT' bulbs gave an average life of 1512 hours with a standard deviation of 80 hours. Is there a significant difference in the mean life of the two makes of bulbs?

42.Two samples of 100 electric bulbs each has a means ]500 and 1550, Standard deviation 50 and 60. Can it be concluded that two brands differ significantly at 1% level of significance in equality?

43. You are given the following information relating to purchase of bulbs from two manufacturers A and B.

Manufacturer No. of Bulbs boushtMean life Standard deviation

A 100 2,950 hours 100 hours

B 100 2,970 hours 90 hours

Is there a significant difference in the mean life of two makes of bulbs? [Take a = 0.05]

44. Theme an produce of wheat of a sample of 100fieldsis 200lb. per acre with a standard deviation of 10 lb. Another sample of 150fieldsgivesthemeanat 220lb. with a standard deviation of 12lb. Assuming the standard deviation of the mean field at 11 lb. for the universe, find at 1% level if the two results are consistent.