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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

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

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### 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**.
Transcribed Image Text:### 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**.
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