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Suppose that a local band is looking to increase its social media presence. The band's manager hopes to attract new fans by having current fans share the band's updates and videos on Facebook, and he wants to estimate the average number of Facebook friends that fans of the band have. To do this, he selects a random sample of n = 10 fans from the band's Facebook page and records how many friends they have. The rounded friend counts for these 10 fans are represented in the stem and leaf plot, where the stems represents the hundreds and the leaves represent the tens. 1 23 543 4 3 5 6 4 7 9 9 5 8 6 Leaf Unit = 10 Using his raw data, he calculates a sample mean of x = 405.0 and a sample standard deviation of s = 189.3. Additionally, suppose that Facebook has reported that the standard deviation for the number of Facebook friends for all users is o = 203.4. The band's manager plans to use this information to construct a 95% z-confidence interval for the mean friend count for fans of the band. Is this an appropriate use of a z-confidence interval? Yes, because the population standard deviation for the number of Facebook friends for all users is given and there are no outliers in the data set. No, because the sample standard deviation is different from the standard deviation for all Facebook users. No, because the sample size is too small given the distribution of the number of Facebook friends is not known to be normal. Yes, because sample means from any distribution are always normally distributed regardless of sample size as long as there are no outliers. No, because a sample that only includes fans of the band is not random.

Suppose that a local band is looking to increase its social media presence. The band's manager hopes to attract new fans by having current fans share the band's updates and videos on Facebook, and he wants to estimate the average number of Facebook friends that fans of the band have. To do this, he selects a random sample of n = 10 fans from the band's Facebook page and records how many friends they have. The rounded friend counts for these 10 fans are represented in the stem and leaf plot, where the stems represents the hundreds and the leaves represent the tens. 1 23 543 4 3 5 6 4 7 9 9 5 8 6 Leaf Unit = 10 Using his raw data, he calculates a sample mean of x = 405.0 and a sample standard deviation of s = 189.3. Additionally, suppose that Facebook has reported that the standard deviation for the number of Facebook friends for all users is o = 203.4. The band's manager plans to use this information to construct a 95% z-confidence interval for the mean friend count for fans of the band. Is this an appropriate use of a z-confidence interval? Yes, because the population standard deviation for the number of Facebook friends for all users is given and there are no outliers in the data set. No, because the sample standard deviation is different from the standard deviation for all Facebook users. No, because the sample size is too small given the distribution of the number of Facebook friends is not known to be normal. Yes, because sample means from any distribution are always normally distributed regardless of sample size as long as there are no outliers. No, because a sample that only includes fans of the band is not random.

MATLAB: An Introduction with Applications
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 that a local band is looking to increase its social media presence. The band's manager hopes to attract new fans by having current fans share the band's updates and videos on Facebook, and he wants to estimate the average number of Facebook friends that fans of the band have. To do this, he selects a random sample of n = 10 fans from the band's Facebook page and records how many friends they have. The rounded friend counts for these 10 fans are represented in the stem and leaf plot, where the stems represents the hundreds and the leaves represent the tens. 1 5 2 3 4 5 6 4 7 9 σ со соди 4 3 3 9 5 8 6 Leaf Unit = 10 Using his raw data, he calculates a sample mean of x = 405.0 and a sample standard deviation of s = 189.3. Additionally, suppose that Facebook has reported that the standard deviation for the number of Facebook friends for all users is 203.4. The band's manager plans to use this information to construct a 95% z-confidence interval for the mean friend count for fans of the band. Is this an appropriate use of a z-confidence interval? Yes, because the population standard deviation for the number of Facebook friends for all users is given and there are no outliers in the data set. No, because the sample standard deviation is different from the standard deviation for all Facebook users. No, because the sample size is too small given the distribution of the number of Facebook friends is not known to be normal. Yes, because sample means from any distribution are always normally distributed regardless of sample size as long as there are no outliers. No, because a sample that only includes fans of the band is not random.
Transcribed Image Text:Suppose that a local band is looking to increase its social media presence. The band's manager hopes to attract new fans by having current fans share the band's updates and videos on Facebook, and he wants to estimate the average number of Facebook friends that fans of the band have. To do this, he selects a random sample of n = 10 fans from the band's Facebook page and records how many friends they have. The rounded friend counts for these 10 fans are represented in the stem and leaf plot, where the stems represents the hundreds and the leaves represent the tens. 1 5 2 3 4 5 6 4 7 9 σ со соди 4 3 3 9 5 8 6 Leaf Unit = 10 Using his raw data, he calculates a sample mean of x = 405.0 and a sample standard deviation of s = 189.3. Additionally, suppose that Facebook has reported that the standard deviation for the number of Facebook friends for all users is 203.4. The band's manager plans to use this information to construct a 95% z-confidence interval for the mean friend count for fans of the band. Is this an appropriate use of a z-confidence interval? Yes, because the population standard deviation for the number of Facebook friends for all users is given and there are no outliers in the data set. No, because the sample standard deviation is different from the standard deviation for all Facebook users. No, because the sample size is too small given the distribution of the number of Facebook friends is not known to be normal. Yes, because sample means from any distribution are always normally distributed regardless of sample size as long as there are no outliers. No, because a sample that only includes fans of the band is not random.
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