### Hypothesis Testing with Unknown Population Standard Deviation#### Question:Suppose you were performing a single sample hypothesis test for a mean with an unknown population standard deviation and a sample size of 25. Which of the following distributions should you use?- F-distribution- Z-distribution- T-distribution- Chi-Squared distribution#### Explanation:In statistics, when conducting a single sample hypothesis test for a mean and the population standard deviation is unknown, the choice of distribution depends on the sample size. If the sample size is small (less than 30), the T-distribution is generally used. This is because the T-distribution accommodates the additional uncertainty introduced by estimating the population standard deviation from the sample.For a sample size of 25, which is considered small, and given that the population standard deviation is unknown, the correct distribution to use is the **T-distribution**. - **F-distribution**: Typically used for comparing two variances or in the context of ANOVA.- **Z-distribution**: Used when the population standard deviation is known, or the sample size is large (typically n > 30).- **T-distribution**: Used for hypothesis tests involving small samples and an unknown population standard deviation.- **Chi-Squared distribution**: Used in tests of independence, goodness-of-fit, and for estimating variances.Thus, the appropriate choice for this scenario is the **T-distribution**.

Sample hypothesis test for mean that isH0 : with unknown population standard deviation s and sample…

Answered: Suppose you were performing a single…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Suppose you were performing a single sample hypothesis test for a mean with an unknown population standard deviation and a sample size of 25. Which of the following distributions should you use? F-distribution Z-distribution T-distribution Chi-Squared distribution