1%= 2.58
S. E= √(npq)
Test of significance= diff/S. E
S. Eₚ= √{pq/n}
S. E of the difference between the proportions:
S. E(p₁ - p₂)= √{pq(1/n₁ + 1/n₂) where p= (n₁p₁ + n₂p₂)/(n₁ + n₂)
e.g., diff/S.E or (p₁ - p₂)/S. E
S. E of mean = s.d/√n
S. E of the difference between sample means: √{σ²(1/(n₁ + 1/n₂)}
1) in 324 throws of a six-faced die odd point appeared 181 times. Would you say that die is "fair"? (5% level ) 2.1
2) 160 heads and 240 tails were obtained in tossing a coin 400 times. Find a 1% confidence interval for the probability of a head. Does this appear to be true coin ? 4
3) In a sample of 500 people from a village in Rajasthan, 280 are found to be rice eaters and the rest wheat eaters. Can we assume that both are food articles are equally popular ? (1% level ) 2.7
4) In a hospital full 480 female and 520 male babies were born in a week. Do these figures confirm the hypothesis that males and females are born in equal numbers ? (5% level) 1.265
5) 500 apples are taken to random from a large basket and 50 are found to be bad. Estimate the proportion of bad apples in the basket. 0.013
6) In a random sample of 1000 person from town A, 400 are found to be consumers of wheat. In a sample of 800 from Town B, 400 are to be found to be consumers of wheat . Do these data reveal a significant difference between Town A and town B, so far as the proportion of wheat consumers is concerned? (1% level). 4.167
7) In a random sample of 500 persons from Maharashtra, 200 are found to be consumers of vegetable oil. In another sample of 400 persons from Gujarat, 200 are found to be consumers of vegetable oil. Discuss whether the data reveal a significant difference between Maharashtra and Gujarat so far as the proportion vegetable oil consumers is concerned. (1% level)
8) Before an increase in excise duty on a tea 400 people out of sample of 500 persons were found to be tea drinkers. After an increase in the duty , 400 persons one known to be tea drinkers in a sample of 600 people. Do you think that there has been significant decrease in the consumption of the consumption of tea after the increasing in the excise duty. (1% level ). 5.2
9) A machine puts out 10 imperfect articles in a sample of 200, After the machine is overhauled it puts out 4 imperfect articles in a batch of 100. Has the machine been improved ? (5% level). 0.388
10) 500 articles from factory are examined and found to be 2% defective. 800 similar articles for a second factory are found to have only 1.5% defectives . Can it reasonably be concluded that the products of the first factory are inferior to these of the second. 0.78
11) There are 1000 students college. Out of 20000 in the whole University, in a study 200 were found smokers in the college and 1000 in the whole University. Is there a significant difference between the proportion of smokers in the college and university ? (1% level). 22.39
12) A sample of 100 iron rods is said to be drawn from a large number of rods whose lengths are normally distributed with mean 3 ft, and standard deviation 0.6 ft. If the sample mean is 3.2 ft., can the sample be regarded as a truly random sample? (1%). 3.33
13) A sample of 100 students is taken from a large population. The mean height of these students is 64 inches and the standard deviation 4 inches. Can it reasonably regarded that in the population mean height is 66 inches. (1% level)
14) 400 labourers were selected at random from a certain district. Their median income was Rs140.5 p.m with standard deviation of Rs25.2. Do you believe that the average income of the labour community in the district is Rs150 ? (1% level). 6.01
15) Random samples drawn from two countries gave the following data relating to height of adult males:
Country A country B
Mean height(in inches) 67.42 67.25
Standard deviation 2.58 2.5
Number of observations 1000 1200
Is the difference between the mean height significant? (5% level). 1.55
16) A man buys 100 electric bulbs each of two well-known makes, taken at random from stock for testing purposes . He finds that 'make A' has a mean life of 1300 hours with a standard deviation of 82 hours, and 'make B' has a mean life of 1248 hours with a standard deviation of 93 hours. Discuss the significance of these results. (1% level). 4.19
17) 490 men students and 450 female students appeared at an examination in statistics. The mean and standard deviation in marks of male students are 54.3 and 17.5 respectively whereas those of female students are 50.6 and 18.0. Is there a significant difference in marks of male and female students? (1% level). 3.19
18) In a survey of buying, 400 women shoppers are chosen at random in supermarket A located in a certain section of Bombay city. Their average monthly food expenditure is Rs400 with a standard deviation of Rs 12. For 400 women shoppers chosen at random in supermarket B in another section of the city, the average monthly food expenditure is Rs395 with a standard deviation of Rs15. Test at a level of 0.05, whether the average food expenditure of the two populations of shoppers from which the samples were obtained are equal. 5.21
19) A potential buyer of electric bulbs bought 200 bulbs , 100 bulbs each of two brands. Upon testing these he found that brand A had a mean life of 1210 hours with a standard deviation 40 hours whereas brand B had a mean life of 1250 hours with a standard deviation of 60 hours. Can the buyer be quiet certain that the two brands differ significantly in quality ? (1% level). 5.55
