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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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Please label each part

For Part D here is the last answer choice: The Student's t-distribution should be used because the sample size is small.

$A sample of 13 small bags of the same brand of candies was selected. Assume that the population distribution of bag weights is normal. The weight of each bag was then recorded. The mean weight was 3 ounces with a standard deviation of 0.13 ounces. The population standard deviation is known to be 0.1 ounce. NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) **Part (a)** Find the following. (Round your answers to two decimal places.) (i) $ \overline{x} = $ (ii) $ \sigma = $ (iii) $ s_x = $ --- **Part (b)** In words, define the random variable $ X $. - ○ the number of candies in a bag - ○ the mean weight of the candies - ○ the weight, in ounces, of one bag of candy - ○ the weight, in ounces, of a piece of candy --- **Part (c)** In words, define the random variable $ \overline{X} $. - ○ the mean number of candies from each bag that weigh 3 ounces - ○ the mean weight, in ounces, of the pieces of candy - ○ the mean weight, in ounces, for the sample of 13 bags - ○ the mean number of candies for the sample of 13 bags --- **Part (d)** Which distribution should you use for this problem? (Round your answers to three decimal places.) $ \overline{X} \sim N \, ( \, \_\_\_\_\_\_\_\_\_\_ \, , \, \_\_\_\_\_\_\_\_\_\_ \, ) $ Explain your choice. - ○ The Student's t-distribution should be used because the sample standard deviation is given. - ○ The standard normal distribution should be used because the population standard deviation is known. - ○ The standard normal distribution should be used because the sample standard deviation is known.$

Transcribed Image Text:A sample of 13 small bags of the same brand of candies was selected. Assume that the population distribution of bag weights is normal. The weight of each bag was then recorded. The mean weight was 3 ounces with a standard deviation of 0.13 ounces. The population standard deviation is known to be 0.1 ounce. NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) **Part (a)** Find the following. (Round your answers to two decimal places.) (i) $ \overline{x} = $ (ii) $ \sigma = $ (iii) $ s_x = $ --- **Part (b)** In words, define the random variable $ X $. - ○ the number of candies in a bag - ○ the mean weight of the candies - ○ the weight, in ounces, of one bag of candy - ○ the weight, in ounces, of a piece of candy --- **Part (c)** In words, define the random variable $ \overline{X} $. - ○ the mean number of candies from each bag that weigh 3 ounces - ○ the mean weight, in ounces, of the pieces of candy - ○ the mean weight, in ounces, for the sample of 13 bags - ○ the mean number of candies for the sample of 13 bags --- **Part (d)** Which distribution should you use for this problem? (Round your answers to three decimal places.) $ \overline{X} \sim N \, ( \, \_\_\_\_\_\_\_\_\_\_ \, , \, \_\_\_\_\_\_\_\_\_\_ \, ) $ Explain your choice. - ○ The Student's t-distribution should be used because the sample standard deviation is given. - ○ The standard normal distribution should be used because the population standard deviation is known. - ○ The standard normal distribution should be used because the sample standard deviation is known.

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According to the sum, A sample of 13 small bags of the same brand of candles was selected. It is assumed that the population distribution of bag weights is normal. The weight of each bag was recorded. The mean weight was 3 ounces with a standard deviation of 0.13 ounces. The population standard deviation is known to be 0.1 ounce.

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