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Sampling Distribution and Estimation
Semester
Subject
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Important Questions
Important Questions
Sampling Distribution and Estimation
Asked in 2081Short Question5 Marks
1.
Define confidence level in estimation. A quality control inspector collected a random sample of 400 tubes of toothpaste from the production line and found that 20 of the tubes had leaks from the tail end. Construct 96% confidence interval for the percentage of all the toothpaste tubes that had leakage and interpret the result. [5]
Asked in 2080Short Question5 Marks
2.
Define Central limit theorem. The life of a certain brand of an electric bulb may be considered a random variable with mean 1350 hours and standard deviation 550 hours. Using central limit theorem, find the probability that the average life time of 100 bulbs exceeds 1440 hours. [5]
Asked in 2080Short Question5 Marks
3.
What do you understand by estimation? If we want to determine average mechanical aptitude of a large group of workers, how large a random sample is needed to be able to assert with probability 0.95 that the sample mean will not differ from the true mean by more than 2.0 points? Assume that population standard deviation is 30. [5]
Asked in 2079Short Question5 Marks
4.
An effort to estimate the mean amount per customer for dinner at a major Atlanta restaurant, data were collected for a sample of 49 customers and sample mean is found at 24.80. Assume population standard deviation is 5. a. Compute standard error of mean. b. Find 95% confidence interval estimate for the population mean. [5]
Asked in 2078Short Question5 Marks
5.
A survey was conducted among 70 students studying B.Sc. CSIT in some colleges randomly. Among them, 50 students secured more than 80% marks in statistics. Compute 99% and 95% confidence intervals for the population proportion of students who secured more than 80% marks in subject statistics, and comment on the results. [5]
Asked in 2078Long Question10 Marks
6.
Explain the sample distribution of mean with reference to some numerical example. Illustrate the practical implications of the Central Limit Theorem (CLT) in inferential statistics. [10]
Asked in 2077Short Question5 Marks
7.
A machine produce metal rods used in an automobile suspension system. A random sample of 6 rods is selected and diameter is measured. The measuring data( in millimeters) are as follows. Assuming that the sample drawn from the normally distributed population. Find 95% two sided confidence interval on the mean rod diameter, and interpret the result with reference to the given problem.
[5]
Asked in 2077Short Question5 Marks
8.
A study of 1000 computer engineers conducted by their professional organization reported that 300 stated that their firms’ greatest concern was to uplift the professional quality of work. In order to conduct a follow up study to estimate the population proportion of computer engineers to fulfill their greatest concern within ±0.01 with 99% confidence interval, how many computer engineers would be required to be surveyed? [5]
Asked in 2077Long Question10 Marks
9.
Describe the concept of sampling distribution of mean with reference to the population data (20, 21, 22 & 23) of size 4. In order to explain this, perform simple random sampling with replacement taking all possible samples with sample size n = 2. While describing the sampling distribution following issues will be covered: a. population mean & population variance, and its distribution b. Sample mean & sample variance, and its distribution c. Comparison of population mean and sample mean; population variance and sample variance; population distribution and sampling distribution based on the given data. d. Standard error of mean e. Final comments based on your result [10]
Asked in 2075Short Question5 Marks
10.
A manufacturer of computer paper has a production process that operates continuously throughout an entire production shift. The paper is expected to have an average length of 11 inches and standard deviation is known to be 0.01 inch. Suppose random sample of 100 sheets is selected and the average paper length is found to be 10.68 inches. Set up 95% and 90% confidence interval estimate of the population average paper length. [5]
Asked in 2075Short Question5 Marks
11.
Determine the minimum sample size required so that the sample estimate lies within 10% of the true value 95% level of confidence, when coefficient of variation is 60% [5]