If the sample size is 13 what condition must be satisfied to compute the confidence interval?
The sample size of 13 must be large enough to ensure that the sampling distribution of the sample mean is approximately normal. Additionally, the sample must be randomly selected from the population of interest.
To compute a confidence interval, certain conditions must be satisfied. For a sample size of 13, the following conditions need to be met:
1. Random sample: The data must be collected from a random sample, meaning that each individual in the population has an equal chance of being selected.
2. Independence: The observations within the sample should be independent of each other. This means that the values collected should not be influenced by one another.
3. Sufficiently large sample: Although there is no minimum requirement for sample size, a general guideline is that the sample should be large enough for the sampling distribution of the sample mean to be approximately normal. For most cases, a sample size of 30 or greater is considered sufficient. However, for smaller samples sizes, as in your case with a sample size of 13, additional assumptions and calculations may be necessary.
4. Normality of the population (optional): If the population from which the sample is drawn is normally distributed (or the sample size is large enough), the population distribution does not need to be known. However, if the sample size is small and the population is not normally distributed, additional assumptions and calculations, such as the t-distribution, may be required.
It is important to note that the specific conditions required for computing a confidence interval may vary depending on the type of data and the statistical method being used.
To compute a confidence interval when the sample size is 13, there are two main conditions that need to be satisfied:
1. The data should be approximately normally distributed: In order to use the methods of hypothesis testing and constructing confidence intervals, the data should follow a normal distribution. This assumption can be checked by visual inspection of the data or by conducting statistical tests, such as the Shapiro-Wilk test or the Kolmogorov-Smirnov test.
2. The sample size should be sufficiently large: While there is no strict threshold for what constitutes a "sufficiently large" sample size, the general guideline is that the sample size should be at least 30. However, if the data satisfy the normality assumption, a slightly smaller sample size can be acceptable.
If these conditions are not met, alternative methods or techniques might be appropriate, such as non-parametric tests or bootstrapping methods.