The
determination of sample size for estimating a population mean or population
proportion is a crucial question. By selecting a sample size lower than the
correct size may affect reliability and higher size will mean more cost and
time. The determination of the size of a sample is the most important factor
for the purposes of estimation of the value of the population parameters.
In order to determine the sample
size for estimating population mean, the following factors must be known.
(i)
The desired confidence level (Z)
(ii)
The permissible sampling error (u-ẍ)
denoted by e
(iii)
The standard deviation σ
or s.
We
know
Z=
where std. error =
where std. error =
Similarly
for determing the sample size for estimating the population proportion, the
following factors must be known.
(i)
The desired confidence level (Z)
(ii)
The permissible sampling error e=P-P1
(iii)
The estimated true proportion of success
(p)
We
Know
DETERMINATION OF SAMPLE SIZE.
- 1. Mr. X wants to determine on the basis of sample study. The average time required to complete a certain job so that he may be 95% confident that the mean may be with in ±2 days of the true mean. The population variance is 64 days. How large should the sample be for his study. Ans. n = 62
- 2. A company wants to determine the average time to complete a certain job. The past record show that the S.D of the completion time for all the workers in the company has been 10 days and there is no reason to believe that this would have changed. However, the company feels that because of the procedural changes the mean would have changed. Determine the sample size so that the company may be 95% confident that the sample average remains with in ±2 days of the mean. Ans. n = 97
- 3. A Pathologist wants to determine on the basis of sample study the mean time required to complete a certain analysis so that he may be 98% confident that the mean may remain with in ±3 days of true mean. As per the available record, the population variance is 81 days. a) What must be the size of sample for his study? b) How large a sample would be required if the precision is to be doubled. Ans. a) 49 b) 196.
- 4. With a sample size of 400, the standard error of mean is 2. What sample size would be required so that we could be 95% confident, that the population mean is with in ±3.5 of sample mean? Ans. n = 502.
- 5. A Cigaratte manufacturer wishes to use a random sample to estimate the average Nicotin content. The sampling error should not be more than 1 milligram above or below the true mean with a 99% confidence The population S.D is 4 milligram what sample size should the company use in order to satisfy these requirements? Ans. n =107.
- 6. A firm wishes to estimate with a maximum allowable error of 0.05 and a 98% level of confidence. The proportion of consumer who prefer its product. How large a sample will be required in order to make such an estimate if the preliminary sales report indicate that 25% of all consumers prefer the firms product. Ans. n = 407
- 7. A company believes that it holds about 30% share of colour TV market in a city. The company wishes to get a precise estimate of its share with in a margin of error 2%. a) How large a no. of household should be surveyed to get the desired estimate with a confidence of 95%? b)If the cost of contacting a household is Rs.20 what will be the total cost of the survey? c) If the budget for the survey is limited to Rs.10,000 what accuracy can be obtained by a survey with in the budget? Ans. a) 2017 b) 40340 c) 0.040.
- 8. The production manager of a manufacturing company wants to access the percentage of items which do not meet the specifications and are thus labelled as defective. He wants to be 95% confident that the percentage has been estimated to be within 1% from the true value. What is the most conservative sample size needed for the situation? Ans. n = 9604
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