Answered: A sample of 15 small bags of the same…

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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$### Understanding Sampling Distribution A sample of 15 small bags of the same brand of candies was selected. Assume that the population distribution of bag weights is normal. Each bag's weight was recorded. The mean weight was 2 ounces with a standard deviation of 0.12 ounces. The population standard deviation is known to be 0.1 ounce. **NOTE:** When using a Student's t-distribution, assume the underlying population is normally distributed. Normally, you should first confirm this assumption. #### Part (a) 1. $\bar{x} =$ [Mean of the sample] 2. $\sigma =$ [Population standard deviation] 3. $s_x =$ [Sample standard deviation] 4. $n =$ [Sample size] 5. $n - 1 =$ [Degrees of freedom] #### Part (b) - Explanation not provided. #### Part (c) - Explanation not provided. #### Part (d) **Choosing the Distribution** - Which distribution should you use for this problem? (Round your answers to three decimal places.) \[\bar{X} \sim \left( [Mean], [Standard Error] \right)\] **Explain Your Choice:** - The correct option is: - The standard normal distribution should be used because the population standard deviation is known. **Explanation:** - Although both the population and sample standard deviations are given, using the standard normal distribution will result in a more accurate interval. #### Part (e) - Explanation not provided. This example emphasizes the importance of identifying the correct distribution to use when the population standard deviation is known. By understanding and practicing such scenarios, one can make more accurate statistical inferences.$

Transcribed Image Text:### Understanding Sampling Distribution A sample of 15 small bags of the same brand of candies was selected. Assume that the population distribution of bag weights is normal. Each bag's weight was recorded. The mean weight was 2 ounces with a standard deviation of 0.12 ounces. The population standard deviation is known to be 0.1 ounce. **NOTE:** When using a Student's t-distribution, assume the underlying population is normally distributed. Normally, you should first confirm this assumption. #### Part (a) 1. $\bar{x} =$ [Mean of the sample] 2. $\sigma =$ [Population standard deviation] 3. $s_x =$ [Sample standard deviation] 4. $n =$ [Sample size] 5. $n - 1 =$ [Degrees of freedom] #### Part (b) - Explanation not provided. #### Part (c) - Explanation not provided. #### Part (d) **Choosing the Distribution** - Which distribution should you use for this problem? (Round your answers to three decimal places.) \[\bar{X} \sim \left( [Mean], [Standard Error] \right)\] **Explain Your Choice:** - The correct option is: - The standard normal distribution should be used because the population standard deviation is known. **Explanation:** - Although both the population and sample standard deviations are given, using the standard normal distribution will result in a more accurate interval. #### Part (e) - Explanation not provided. This example emphasizes the importance of identifying the correct distribution to use when the population standard deviation is known. By understanding and practicing such scenarios, one can make more accurate statistical inferences.

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