Math Problem Solver

1.a.Before an increase in excise duty on tea, 800 persons out of a sample of 1000 persons were found to be tea drinkers. After an increase in excise duty, 800people were tea drinkers in a sample of 1200 people. Using standard error of proportion, state whether there is a significant decrease in the consumption of tea after the increase in excise duty?

b.The mean weekly sales of soap bars in departmental stores was 146.3 bars per store. After an advertising campaign the mean weekly sales in 22 stores for a typical week increased to 153.7 and showed a S.D. of 17.2. Was the advertising campaign successful?

2.a.Below are given the gain in weights (in lbs) of pigs fed on two diets A and B:

Diet-A 25 32 30 34 24 14 32 24 30 31 35 25 - - -

Diet-B 44 34 22 10 47 31 40 30 32 35 18 21 35 29 22

Test, if the two diets differ significantly as regards their effect on increase in weight.(5% Level of significant)

b.4 coins were tossed 130 times and the following results were obtained.

No. of heads 0 1 2 3 4

Observed frequencies 17 52 54 31 6

Use the assumption that coins are balanced , find the expected frequencies of 0, 1,s 2, 3 or 4 heads and test the goodness of fit (at 5% LOS).

3.a.A random sample of size 25 from a normal population has the mean = 47.5 and the standard deviation S = 8.4. Does this information tend to support or refute the claim that the mean of the population is μ = 42.5 ?

b.A study shows that 16 out of 200 tractors produced one assembly line required extensive adjustments before they could be shopped, while the same was true for 14 of 400 tractors produced on an other assembly line. At the 0.01 level of significance, does this support the claim that the second production line does superior work?

4.a.Pumpkins were grown under two experimental conditions. Two random samples of 11 and 9 pumpkins. Show the sample standard deviations of their weights as 0.8 and 0.5 respectively. Assuming that the weight distributions are normal, test the hypothesis that the true variances are equal.

b. From the following data, find whether there is any significant liking I in the habit of taking soft drinks among the categories of employe

Soft Drinks Clerks Teachers Officers

Pepsi 10 25 65

Thumsup 15 30 65

Fanta 50 60 30

5.a.A sample of 900 members has mean 3.5 CMS, and standard deviation 2.61 CMS. Can it be concluded that the sample has drawn from the population of members with a mean 3.2 CMS and standard deviation 2.61 CMS?

b.Below are given the gain in weights (in lbs.) of pigs fed on two diets A and B:

Diet-A 25 32 30 34 24 14 32 24 30 31 35 25 - - -

Diet-B 44 34 22 10 47 31 40 30 32 35 18 21 35 29 22

Test, if the two diets differ significantly as regards their effect on increase in weight.

6.a.The mean weekly sales of Powder in Supermarket was 146.3 tins. After a special advertising campaign the mean weekly sales in 22 branches in a week increased to 153.7 tins and showed a S.D. of 17.2 tins. Was advertising campaign successful?

b.The table below gives the number of aircraft accidents that occurred during the Various days of the week. Test whether the accidents are uniformly distributed over the week.

Days Mon Tues Wed Thu Fri Sat

No. of accidents 14 18 12 11 1 14

7.a.A sample of heights of 6400 English men has a mean of 67.85 inches and S.D. 2.56 inches, while another sample of heights of 1600, Australians has a mean of 68.55 inches and a S.D. of 2.52 inches. Do the data indicate that Australians are on the average, taller than Englishmen ?

b.Random samples of 400 men and 600 women were asked whether they would like to have flyover near their residence. 200 men and 325 women were in favor of the proposal. Test the hypothesis that proportions of men and women were in favor of the proposal are same against that they are not at 5% level

8.a.Two horses A and B were tested according to the time (in seconds) to run a particular track with the following results.

Horse-A 28 30 32 33 33 29 34

Horse-B 29 30 30 24 27 29 -

Test whether the two horses have the same running capacity.(use 5% LOS).

b.A pair of dice are thrown 360 times and the frequency of each sum is indicated below:

Sum 2 3 4 5 6 7 8 9 10 11 12

frequency 8 24 35 37 44 65 51 42 26 14 14

Would you say that the dice are fair on the basis of the chi-square test at 5% level of significance?

9.a.A machine produced 20 defective articles in a batch of 400 articles. After overhauling, it produced 10 defectives in a batch of 300 articles. Has the machine improved?

b.A cigarette manufacturing firm claims that its brand A of the cigarettes outsells its brand B by 8%. If it is found that 42 out of a sample of 200 smokers prefer brand A and 18 out of another random sample of 100 smokers prefer band B.

10.a.The weights of 10 people of a locality are found to be 70,67,62,68,61,68,70,64, 64, kilograms. Is it reasonable to believe that the average weights of the people of locality is greater than 64 kg? Test at 5% level of significance.

b.Two researchers adopted different sampling techniques while investigating some group of students to find the number of students falling in to different intelligence level. The results are as follows:

Researchers Below Average Average Above Average Genius Total

X 86 60 44 10 200

Y 40 33 2 2 100

Total 126 93 69 12 300

Would you say that the sampling techniques adopted by the two researchers are significantly different.