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1. In an intro stats class, students were asked to work in teams of 2 to conduct a survey their peers and perform some statistical analyses. Alex and Morgan decided to work together and ask "How many minutes do you exercise in a week?" Alex asked this question to 10 of their peers and computed a sample mean. Morgan felt like they needed to get a larger sample, so Morgan asked 20 peers (different from those that Alex asked) and computed a sample mean. To get a combined mean, the pair come up with two choices. Alex suggested that they average the two sample means - thus Alex is proposing that mu-hat = (x-bar_Alex + x- bar_Morgan)/2 Morgan suggested that they put all 30 responses into one column in Excel and find the overall mean of the combined sample. a) Show that both Alex and Morgan's estimators are unbiased. b) Determine which estimator has a smaller variance. Show your work.

1. In an intro stats class, students were asked to work in teams of 2 to conduct a survey their peers and perform some statistical analyses. Alex and Morgan decided to work together and ask "How many minutes do you exercise in a week?" Alex asked this question to 10 of their peers and computed a sample mean. Morgan felt like they needed to get a larger sample, so Morgan asked 20 peers (different from those that Alex asked) and computed a sample mean. To get a combined mean, the pair come up with two choices. Alex suggested that they average the two sample means - thus Alex is proposing that mu-hat = (x-bar_Alex + x- bar_Morgan)/2 Morgan suggested that they put all 30 responses into one column in Excel and find the overall mean of the combined sample. a) Show that both Alex and Morgan's estimators are unbiased. b) Determine which estimator has a smaller variance. Show your work.

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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do part 1a and 1b

1. In an intro stats class, students were asked to work in teams of 2 to conduct a survey of their peers and perform some statistical analyses. Alex and Morgan decided to work together and ask "How many minutes do you exercise in a week?" Alex asked this question to 10 of their peers and computed a sample mean. Morgan felt like they needed to get a larger sample, so Morgan asked 20 peers (different from those that Alex asked) and computed a sample mean. To get a combined mean, the pair come up with two choices. Alex suggested that they average the two sample means - thus Alex is proposing that mu-hat = (x-bar_Alex + x- %3D bar_Morgan)/2 Morgan suggested that they put all 30 responses into one column in Excel and find the overall mean of the combined sample. a) Show that both Alex and Morgan's estimators are unbiased. b) Determine which estimator has a smaller variance. Show your work. 2. Find the method of moments estimators for a and b for the continuous uniform distribution. (see page 136).
Transcribed Image Text:1. In an intro stats class, students were asked to work in teams of 2 to conduct a survey of their peers and perform some statistical analyses. Alex and Morgan decided to work together and ask "How many minutes do you exercise in a week?" Alex asked this question to 10 of their peers and computed a sample mean. Morgan felt like they needed to get a larger sample, so Morgan asked 20 peers (different from those that Alex asked) and computed a sample mean. To get a combined mean, the pair come up with two choices. Alex suggested that they average the two sample means - thus Alex is proposing that mu-hat = (x-bar_Alex + x- %3D bar_Morgan)/2 Morgan suggested that they put all 30 responses into one column in Excel and find the overall mean of the combined sample. a) Show that both Alex and Morgan's estimators are unbiased. b) Determine which estimator has a smaller variance. Show your work. 2. Find the method of moments estimators for a and b for the continuous uniform distribution. (see page 136).
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