From question 1-7, no need to explain, just answer; for question 8-14, explain in detail using excel

1. A population consists of four elements 3, 7, 11 and 15. Consider all possible samples of size 2 which can be drawn with replacement from this population. Find population mean and standard deviation.

2 points

a)30, 20

b)36, -4.47

c)9, 4.47

d)36, 20

2. In Q1 find the mean of the sampling distribution of means.

2 points

a)9

b)15

c)36

d)6

3. In Q1, find the variance of the sampling means.

2 points

a)20

b)10

c)15

d)18

4. The mean of a certain normal distribution is equal to the standard error of the mean of samples of 25 from the distribution. Find the probability that the mean of a sample of 49 from the distribution will be negative. Given: Area under standard normal curve to the left of the ordinate at 1.4 is 0.9192.

2 points

a)0.918

b)0.0028

c)0.0808

d)0.9192

5. A sample of 400 male students is found to have a mean height of 171.38 cm. Can it be reasonably regarded as a sample from a large population with mean height 171.17cm and SD 3.30cm? Test at 5%level of significance.

2 points

a)z=0.165, |z|<1.96 Accept null hypothesis

b)z=1.27, |z|<1.96 Accept null hypothesis

c)z=1.965, |z|>1.96 Reject null hypothesis

d)z=2.65, |z|>1.96 Reject null hypothesis

6. The mean yield of wheat from a district A was 210 kg with SD= 10 kg per acre from a sample of 100 plots. In another district B, mean yield was 220 kg with SD of 12 kg per acre from a sample of 150 plots. Assuming that the SD of the yield in the entire state was 11 kg test whether there is any significant difference between the mean yield of crops in the two districts. Test at 1% level of significance.

2 points

a)z= 1.42, Critical value, zo= 1.96, |z|< zo, Accept Null hypothesis

b)z= 7.42, Critical value, zo= 1.96, |z|>zo, Reject Null hypothesis

c)z= -7.04, Critical value, zo= 2.58, |z|> zo, Reject Null hypothesis

d)z= 2.42, Critical value, zo= 2.58, |z|< zo, Accept Null hypothesis

7. In a certain city 100 men in a sample of 400 were found to be smokers. In another city the number of smokers was 300 in a random sample of 800. Does this indicate that there is a greater proportion of smokers in the second city than in the first ? Test at 1% level of significance.

3 points

a)z= 2.42, Critical value, zo= 1.96, |z|>zo, Accept Null hypothesis

b)z= 3.42, Critical value, zo= -1.645, |z|> zo, Reject Null hypothesis

c)z= -4.31, Critical value, zo= -2.33, |z|> zo, Reject Null hypothesis

d)z= 1.42, Critical value, zo= -2.33, |z|< zo, Accept Null hypothesis

8. Find the mean & Standard deviation for the following data using excel builtin function: 25, 50, 45, 30, 70,42,36,48,34,60.

1 point

a)Mean =4.4, SD= 1.3

b)Mean= 44, SD= 13.076

c)Mean= 49, SD=12.08

9. Calculate Mean and SD for the following data using Excel: x: 4, 5, 6, 7, 8, 9, 10; Corresponding frequency f: 6, 12, 15, 28, 20, 14, 5.

1 point

a)Mean=7.06, SD=1.541

b)Mean= 7, SD= 0.541

c)Mean= 7.25, SD= 2.541

10. Lifestyle conducted a field survey covering 200 respondents on how much is the satisfaction level of a particular brand is important to them. The results of the survey are: Very satisfactory 50, Satisfactory 60, Neither satisfactory nor dis-satisfactory 20, Dis-satisfactory 40, Very dis- satisfactory 30. Is there any significant difference in importance rating for satisfaction level among the respondents at 1% level of significance?

1 point

a)Chi Square = 25, Degree of freedom 5, Ho is rejected.

b)Chi square= 25, Degree of freedom 4, Ho is rejected.

c)Chi square= 13.277, Degree of freedom 4, Ho is accepted.

11. A certain drug is claimed to be effective in curing cold. In an experiment on 164 people with cold, half of them were given the drug 1 and half of them given drug 2. The patients reactions to the treatment are recorded as Drug 1: Recovered 104, Harmed 20, No effect 40; Drug 2: Recovered 88, Harmed 24, No effect 52. Test the hypothesis that the drug 1 is no better than drug 2 for curing cold.

1 point

a)Chi square = 3.69, df=5, Ho is accepted.

b)Chi square= 3.264, df= 2, Ho is accepted.

c)Chi square= 5.99, df= 3, Ho is rejected.

12. It is desired to compare 3 hospitals with regards to the number of deaths per quarter. A sample of death records were selected from the records of each hospital and number of deaths are given below. From these data. suggest a difference in the number of death per quarter among three hospitals: Hospital I: 8, 10, 7, 14,11; Hospital II: 7, 5, 10, 9, 9; Hospital III: 12, 9, 13, 12, 14. Test at 5% level of significance.

1 point

a)SSC=40, SSE=60, F=4, Ho is rejected.

b)SSC=4, SSE=16, F=2, Ho is rejected.

c)SSC=40, SSE=10, F=4, Ho is rejected.

13. Set up a two way ANOVA table for the following per hectare yield for 4 varieties of wheat A, B, C & D on 3 plots: Plot I: yield of A 3, B 4, C 6, D 6. Plot II: yield of A 6, B 4, C 5, D 3. Plot III: yield of A 6, B 6, C 4, D 7.

1 point

a)F1=0.663, F2=0.08

b)F1=0.08, F2=0.663

c)F1= 0.22, F2=2.64

14. The study of performance of 3 detergents(A, B & C) in 3 different water temperatures were recorded with specially designed equipment. The following whiteness readings were recorded: Cold water: A 57, B 55, C 67; Warm water: A 49, B 52, C 68; Hot water A 54, B46, C 58. Perform a two way analysis using 5% level of significance given that F at 5%= 6.94.

1 point

a)F1=9.99, F2= 2.33, Ho is rejected in both cases.

b)F1=2.33, F2=9.99, Ho is accepted in both cases.

c)F1=9.85, F2=2.38, Ho is rejected in both cases.