2021 April Q. No. 1b(15 Marks) [Testing of Hypothesis ANOVA Table]
The motor company has four salesperson A,B, C, and D. They are sent to three different places for marketing purposes. The sales in ten thousand of rupees per month are shown below:
Places  Salesperson  
A  B  C  D  
I  15  35  15  15 
II  40  25  20  35 
III  50  30  40  40 
Test whether there is a significant difference in average sales motor due to (i) four different salespersons, (ii) three different places.
2021 April (Back) Q. No. 2 [7.5+7.5 Marks] [Testing of Hypothesis ANOVA Table]
The following table shows the sales (in 0000 Rs) across salesmen and seasons.
Seasons

Salesmen  
A  B  C  D  E  
Summer  20  18  16  23  13 
Winter  30  25  22  15  25 
Monsoon  25  28  18  22  17 
Test at 5% level of significance whether the average sales significantly differs due to(i) Salesmen(ii)Seasons.
2019 August Q. No. 1a (15 Marks) [Testing of Hypothesis ANOVA Table]
A researcher is interested in the effect of several herbicides on the spike weight (ounces) of gladiolus flower. The data is presented below:
Block  Treatments  
I  II  III  IV  
A  1.25  2.05  1.95  1.75 
B  1.73  1.56  2.00  1.93 
C  1.82  1.68  1.83  1.70 
D  1.31  1.69  1.81  1.59 
Test at 5% level of significance whether there. is a significant difference in the gladiolus spike weight due to (i) four blocks and (ii) four treatments.
2019 Back Q. No. 2  2018 January Q. No. 2  2015 Q. No. 2 (15 Marks) [Testing of Hypothesis ANOVA Table]
A company appoints four salesmen A, B, C and D and observes their sales in three seasons Summer, Monsoon and Winter. The figures for their sales (in thousands) are given below.
Season  Salesmen  
A  B  C  D  
Summer  36  36  21  35 
Monsoon  26  28  29  29 
Winter  28  29  31  32 
Test whether there is a significant difference in average sales due to (i) seasons and (ii) salesman.
2018 August Q. No. 2 (15 Marks) [Testing of Hypothesis ANOVA Table]
The following data represents the number of units of production per day turned out by four workmen using three types of machines.
Workmen

types of machine  
X  Y  Z  
A  44  38  47 
B  46  40  52 
C  34  36  44 
D  33  38  46 
Test at 5% level of significance whether there is a significant difference in mean productivity.
a. due to three machines.
b. due to four workmen.
2017 Make up Q.No. 2 (15 Marks) [Testing of Hypothesis ANOVA Table]
The following table presents the sales in three regions due to three salesperson. Test at 5% level of significance whether the average sales due to salespersons or the difference in region are significantly different.
Regions  Salesperson  
R_{1}  200  800  500 
R_{2}  300  400  300 
R_{3}  250  500  400 
7.2016 Q.No. 2(15 Marks) [Testing of Hypothesis ANOVA Table]
The following table shows the yield of the crops along with the type of land and fertilizers.
Fertilizer Type

Type of Land  
1  2  3  4  
I  55  56  58  58 
II  58  56  57  55 
III  58  58  56  59 
Test whether there is a significant difference in the average yield of crop due to (i) four different fertilizers and (ii) three different types of land.
2015 Make up Q.No. 2 (15 Marks) [Testing of Hypothesis ANOVA Table]
The following table presents the sales in three regions due to three salespersons. Test at 5% level of significance whether the average sales are significantly different due to (i) Salespersons and (ii) Regions.
Regions

Sales Person  
C1  C2  C3  
R1  30  70  30 
R2  80  50  40 
R3  100  60  80 
2014 Q.No. 2 (15 Marks) [Testing of Hypothesis ANOVA Table]
A company has four marketing executives ME1, ME2, ME3 and ME4. They work in three cities Kathmandu, Bhaktapur and Patan. The table below shows the sales in ten thousand rupees per month.
City

Maketing executives  
ME1  ME2  ME3  ME4  
Kathmandu  30  70  30  30 
Bhaktapur  80  50  40  70 
Patan  100  60  80  80 
Carry out Two WayANOVA and interpret the results.
2018 June (Makeup) Q. No. 2 (15 Marks) [Testing of Hypothesis chi Squre Test]
Fit a binomial distribution to the following data and test the goodness of it.
X  0  1  2  3  4 
f  28  62  46  10  4 
Critical Analysis/ProblemSolving Questions
2014 Q. No. 5a
Describe about the errors in hypothesis testing.
2021 April Q. No. 3a(15 Marks) [Testing of Hypothesis Z Test]
Suppose the Acme Drug Company develops a new drug, designed to prevent colds. The company states that the drug is equally effective for men and women. To test this claim, they choose a simple random sample of 100women and 200 men from a population of 100,000 volunteers. At the end of the study, 38% of the women caught a cold; and 51% of the men caught a cold. Based on these findings, can we reject the company’s claim that the drug is equally effective for men and women? Use a 0.05 level of significance.
2021 April Q. No. 5b
A researcher has selected two markets, A and B at different locations of a city in order to make a survey on buying habits of customers. 400women shoppers are chosen at random in market A. Their average monthly expenditure on food is found to be Rs. 1050 with a standard deviation of Rs. 44. The corresponding figures are Rs. 1020 and Rs. 56 found respectively in market B where400 men shoppers are chosen at random. Test at 1% level of significance whether the average monthly food expenditure of the two populations of shoppers are equal.
2021 April (Back) Q. No. 4a
A random sample of 100 employees from plant A and a random sample of 150 families from plant B yield the following data on knowing the organizations completely soon after they join plants. Do these data provide sufficient evidence to indicate that, on average, employees in Plant A have had less time than that of employees from Plant B for knowing the organizations completely soon after they join respective plants? ( α = 5%)
Plant  Average time (Months)  Variances 
A  33  900 
B  49  1050 
2019 August Q. No. 3a
An economist was curious if women were more satisfied with their jobs than men. A random sample of 220 workers showed that 46 out of 100women were satisfied with their jobs, and 42 of 120 men were satisfied. Assuming that conditions have been met, test at 5% level of significance the women were more satisfied with their jobs than men.
2019 August Q. No. 5b
An examination was given to 50 students at College A and to 60 students at College B. At A, the mean grade was 75 with a standard deviation of 9, at B; the figures were 79 and 7 respectively. Is there a significant difference between the performance of the students at A and at B, at 0.05 and 0.01 levels of significance?
2019 Back Q. No. 4a  2018 Jan Q. No 5a  2017 Make up Q. No. 3a  2015 Make up 4b
A sample of heights of 6400 Indians has a mean of 67.85 inches and an S.D. of 2.56inches, while a sample of the height of 1600 Japanese has a mean is 68.55 inches and an S.D.of 2.52 inches. Do the data indicate that Japanese are on average taller than Indians?
2018 August Q.No. 5(a)
A researcher conducted a test on the verbal ability of male and female students of campus and found the following information:
Statistics  Male students  Female students 
Sample size  850  550 
Average score  520  540 
Standard deviation  75  80 
Using 5% level of significance, can you conclude that female students have higher verbal ability than male students?
2018 June Make up Q.No. 3a
The mean weight of the sample of 50 packets of the product is 14.5 kg. Test whether the sample is from a batch of packets having a mean weight of 15.6 kg. and a standard deviation of 2.2 kg.
2018 June Makeup Q.No. 4 (b)
The manufacturer of the electronic equipment, based in Patan city, claims, that only 4% of its products are defective. To test the claim of the manufacturer, a random sample of 350 products is taken and found to have 15 defectives. Do you agree with the view of the manufacturer?
10. 2018 January Q.No. 4a
The managing director of a Bank claims that the average time to cash a cheque in that Bank is not more than 8 minutes. To test this claim a researcher took a random sample of 100 customers and found that the mean time to cash a cheque was 10 minutes and the standard deviation was 6.5 minutes. Is the claim of the director true at 1% level of significance?
[4.5]
11. 2016 O.No. 4(a)
A distributor claims that only 4% of the items supplied by him are out of order. A random sample of 300 items contained 18 items out of order. Test the claim of the distributor.
[4.5]
12. 2014 Q.No. 3a
A pharmaceutical firm maintains that the mean time for a drug to take effect is 24 minutes. In a sample of 400 trials, the mean time is 26 minutes with a standard deviation of 4 minutes. Test the hypothesis that the mean time is 24minutes against the alternative hypothesis that is not equal to 24 minutes. Use a level of significance of 0.05.
[4.5]
13.2014 Q.No. 4b
There has been a dispute that the articles produced from two factories
A and B located in Nawalparasi and Nepalgunj are not of same. To settle this dispute an analyst took 1000 articles from factory A which has 3% defectives, likewise, only2% defective articles are found from 1500 articles of factory B. Would you conclude that the products of factory B are superior to those of factory A?
[4.5]