Asked by Naderay Atefi on Jul 29, 2024
Verified
From a population that is normally distributed, a sample of 25 elements is selected and the standard deviation of the sample is computed.For the interval estimation of μ, the proper distribution to use is the
A) normal distribution.
B) t distribution with 25 degrees of freedom.
C) t distribution with 26 degrees of freedom.
D) t distribution with 24 degrees of freedom.
T Distribution
A probability distribution that emerges in the context of estimating the mean for a normally distributed population, applicable when dealing with a small sample size and the population standard deviation is not known.
Degrees of Freedom
The number of independent pieces of information available to estimate another parameter or the number of values in the final calculation of a statistic that are free to vary.
Interval Estimation
A range within which a population parameter is estimated to lie, based on sample data and a certain level of confidence.
- Select the suitable z or t value for estimating confidence intervals, considering the sample size and data provided.
Verified Answer
SS
Sandeep SharmaJul 30, 2024
Final Answer :
D
Explanation :
When estimating the population mean μ from a sample, if the population standard deviation is unknown and the sample size is n, the t distribution with n-1 degrees of freedom is used. Here, with a sample size of 25, the correct choice is the t distribution with 24 degrees of freedom.
Learning Objectives
- Select the suitable z or t value for estimating confidence intervals, considering the sample size and data provided.