Which of the following factors does not usually affect the width of a confidence interval ?
Population size
The width of a confidence interval for a mean is twice the margin of error: \(\text{Width}=2\cdot z\cdot\frac{\sigma}{\sqrt{n}}\).
Sample size affects it: a larger n reduces \(\frac{\sigma}{\sqrt{n}}\) and narrows the interval.
Confidence desired affects it: a higher confidence level (say 99% instead of 95%) raises z and widens the interval.
Variability in the population affects it: a larger \(\sigma\) makes the interval wider, a more homogeneous population makes it narrower.
Population size N does not appear in the formula; it matters only through the finite population correction \(\sqrt{\frac{N-n}{N-1}}\) when the sample is a large share of the population, which is usually not the case, so its effect is negligible.
Hence, the answer is Population size.
Similar Questions
In a study, participants are recruited from local schools in urban area. The study is conducted on saturday so only the saturday working school take part. What type of sample is this ?
Multistage cluster sampling is helpful when :
When a research problem is related to heterogeneous population, the most suitable method is :
A researcher selects a probability sample of 100 out of the total population, it is called :
When the population is divided into subsets such that the units within the subset are as heterogeneous as possible and are as homogeneous as possible among themselves, the sampling method is called as :
The standard error of sample mean based on 100 observations from normal distribution with mean 50 and standard deviation 5 is ............ .
Sampling error can be reduced by :
A magazine printed a survey in its monthly issue and asked readers to fill it out and send it in. Over 1000 readers did so. What is this type of sample called ?
What type of Sampling technique is it when researcher ‘selects samples as and when s/he gets them’ in the process of data collection ?
Which is the sampling technique that allows every unit in the population an equal chance of being selected ?
Important Questions from Sample - Teaching
- Which of these statements does NOT describe snowball sampling correctly?
A. It is a non-probability sampling technique.
B. It is used when the target population is readily available.
C. Initial participants refer others to take part in the study.
D. It ensures equal chance of selection for all individuals.
E. It is commonly used in sociological and qualitative research.
Choose the correct answer from the options given below: - Assertion (A): The larger the sample size, the greater will be the power of the test.
Reason (R) : A large sample size results in smaller standard error of mean.
Codes : - Given below are two statements, one labelled as Assertion (A) and the other labelled as Reason (R). Read the statements and choose the correct answer using the code given below.
Assertion (A) : Findings of a research based on a large sample size of a population being studied can always be generalized to the whole population.
Reason (R) : Sample size does not ensure representativeness. - In a Random Sampling distribution of means :
I. The standard error will decrease as the sample size increases.
II. The standard error will increase as the sample size increases.
III. The mean equals the population mean.
IV. The mean is not equal to the population mean. In a study, participants are recruited from local schools in urban area. The study is conducted on saturday so only the saturday working school take part. What type of sample is this ?
