The failure data for 40 electronic components is shown below:
| Operating Time (in hours) | 0-5 | 5-10 | 10-15 | 15-20 | 20-25 | 25-30 |
| Number of Failures | 5 | 7 | 6 | 4 | 5 | 4 |
| Operating Time (in hours) | 30-35 | 35-40 | 40-45 | 45-50 | ≥50 | |
| Number of Failures | 4 | 0 | 2 | 1 | 2 |
Estimate the reliability, cumulative failure distribution, failure density and failure rate functions.
See Answer →A system has seven independent components and reliability block diagram of it shown as follows:
Find reliability of the system.
See Answer →An office supply company ordered a lot of 400 printers. When the lot arrives the
company inspector will randomly inspect 12 printers. If more than three printers in the
sample are non-conforming, the lot will be rejected. If fewer than two printers are nonconforming, the lot will be accepted. Otherwise, a second sample of size 8 will be
taken. Suppose the inspector finds two non-conforming printers in the first sample and
two in the second sample. Also AQL and LTPD are 0.05 and 0.10 respectively. Let
incoming quality be 4%.
(i) What is the probability of accepting the lot at the first sample?
(ii) What is the probability of accepting the lot at the second sample?
A manufacturer of men’s jeans purchases zippers in lots of 500. The jeans
manufacturer uses single-sample acceptance sampling with a sample size of 10 to
determine whether to accept the lot. The manufacturer uses c = 2 as the acceptance
number. Suppose 3% nonconforming zippers are acceptable to the manufacturer and
8% nonconforming zippers are not acceptable. Find
(i) Probability of accepting a lot of incoming quality 0.04.
(ii) Average outing quality (AOQ), if the rejected lots are screened and all defective
zippers are replaced by non-defectives.
(iii) Average total inspection (ATI).
Differentiate between the autoregressive and moving average models of time series.
See Answer →A system has four components connected in parallel configuration with reliability 0.2, 0.4, 0.5, 0.8. To improve the reliability of the system most, we have to replace the component which reliability is 0.2.
See Answer →If a researcher wants to find the relationship between today’s unemployment and that of 5 years ago without considering what happens in between then the partial autocorrelation is the better way in comparison to autocorrelation.
See Answer →If the effect of summer and winter is not constant on the sale of AC then we use the additive model of the time series.
See Answer →In single sampling plan, if we increase acceptance number then the OC curve will be steeper.
See Answer →The R- chart is suitable when subgroup size is greater than 10.
See Answer →In a class of Statistics, total number of students is 30. Select the linear and circular
systematic random samples of 12 students. The age of 30 students is given below:
Age: 22 25 22 21 22 25 24 23 22 21 20
21 22 23 25 23 24 22 24 24 21 20
23 21 22 20 20 21 22 25
The following data is the data pertaining to a feeding trial on sheep. Treatments
A: Grazing only
B: Grazing + Maize Supplements
C: Grazing + Maize + Protein Supplement P1
D: Grazing + Maize + Protein Supplement P2
E: Grazing + Maize + Protein Supplement P3
Layout and Wool Yield (100 gm) is given as:
| 32(D) | 33(E) | 30(C) | 28(B) | 24(A) |
| 51(C) | 45(D) | 41(A) | 45(E) | 29(B) |
| 41 (E) | 29 (A) | 24 (B) | 36 (D) | 35 (C) |
| 38 (B) | 39(C) | 42(E) | 23(A) | 37(D) |
| 38(A) | 24(B) | 21(D) | 29(C) | 26(E) |
Analyse the design with appropriate method and calculate the Critical Difference for the treatment mean yield.
See Answer →For the given data the yield of the treatment 2 in 3rd block is missing. Estimate the missing value and analyse the data.
| Treatments | Blocks |
| 1 | I II III IV |
| 105 114 108 109 112 113 Y 112 106 114 105 109 |
See Answer →
A manurial trial with six levels of Farmyard Manure (FYM) was carried out in a randomised block design with 4 replications at the experimental station Junagarh with a new study the rate of decomposition of organic matters in soil and its synthetic capacity in soil on cotton crop. The yield per plot in kg for different levels of FYM and replications is given below:
Cotton Yield Per Plot (in Kg)
| Levels of FYM | Replications |
| I II III IV | |
| 1 | 6.90 4.60 4.40 4.81 6.48 5.57 4.28 4.45 6.52 7.60 5.30 5.30 6.90 6.65 6.75 7.75 6.00 6.18 6.50 5.50 7.90 7.57 6.80 6.62 |
Carry out the Analysis of Variance test and draw the conclusions.
See Answer →In order to compare the mileage yields of 3 kinds of Gasoline, several tests were run, and the following results were obtained:
| Gasoline A: | 19 | 21 | 20 | 18 | 21 | 21 |
| Gasoline B: | 23 | 20 | 22 | 20 | 24 | 23 |
| Gasoline C: | 20 | 17 | 21 | 19 | 20 | 17 |
Carry out the Analysis of Variance test and test whether there is significant differences between the average mileage of 3 kinds of gasoline at 5% level of significance.
See Answer →In a population of size N = 5, the values of the population characteristics are 1, 3, 5, 7, 9, a sample of size 2 is drawn. Verify that y is an unbiased estimate of YandV(y) is equal to
V(y)=
A population consists of 10 villages with a total of 212 households. The second column of the accompanying table shows the number of households corresponding to each village. Select a PPS with replacement sample of 6 villages by using the Cumulative Total method:
| Village | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| No. of Households | 35 | 28 | 20 | 25 | 30 | 19 | 10 | 12 | 18 | 15 |
See Answer →
A sample of 100 employees is to be drawn from a population of collages A and B. The population means and population mean squares of their monthly wages are given below:
| Village | Ni | Xi | Si2 |
| Collage A | 400 | 60 | 20 |
| Collage B | 200 | 120 | 80 |
Draw the samples using Proportional and Neyman allocation techniques and compare. Obtain the sample mean and variances for the Proportional Allocation and SRSWOR for the given information. Then Find the percentage gain in precision of variances of sample mean under the Proportional Allocation over the that of SRSWOR.
See Answer →State whether the following statements are true or false and also give the reason in
support of your answer: (5×2=10)
(a)Vopt( st )lies betweenVprop andV (Xst ).and VRandom (Xst).
(b) The total number of all possible samples of size 3 without replacement from a population of size 7 is 21.
(c) While analysing the data of a 5 × 5 Latin Square design the d.f. for ESS is equal
to 16.
(d) In a Two-way Analysis of Variance test with 5 observations per cell having 4
blocks and 4 treatments the degree of freedom for the total variation is 64.
(e) The probability of selection of a sample of n from the population by SRSWOR is
1/ N.
See Answer →
A hospital specialising in heart surgery. In 2022 total of 2000 patients were admitted
for treatment. The average payment made by a patient was Rs 1, 50,000 with a
standard deviation of Rs 25000. Under the assumption that payments follow a normal
distribution, answer the following questions.
(i) The number of patients who paid between Rs 1,40,000 and Rs 1,70,000.
(ii) The probability that a patient bill exceeds Rs 1,00,000.
(iii) Maximum amount paid by the lowest paying one-third of patients.