Textbook exercise: A city’s status and living conditions may affect how its residents perceive their mayor and city council. Dr. Benevita has used data from Statistics Canada to rank larger metropolitan areas against each other. Focusing on unemployment rates, median household income, and crime rates, he has given Calgary an overall positive ranking (low unemployment, high income, and relatively low crime), and Winnipeg an overall negative one (mid-range unemployment, fairly low income, and very high crime). Dr. Benevita has contacted 40 residents of each city to respond to one simple question: “How competent do you believe your municipal leaders are in governing your city?” Participants rated their municipal government on a scale of -3 (completely incompetent) to +3 (completely competent). A perfectly normal distribution around the central, neutral, point would have a mean of 0 and a standard deviation of 1.66. We will use this as our comparison point to determine whether residents of Calgary and Winnipeg have an overall positive or negative view of their municipal government. μ = 0.00, SD = 1.66 1. In Calgary, the 40 surveyed residents gave their municipal leaders a mean rating of 0.65. In Winnipeg, the 40 surveyed residents gave a mean rating of -1.18. 2. complete the 5 steps of Hypothesis Testing twice (once for each city) to answer the two research questions here: Do residents of Calgary have an overall positive view of their municipal government? Do residents of Winnipeg have an overall negative view of their municipal government? In both cases, this will be a 2-tailed test with a .05 significance level. (Despite the fact that our research questions are both directional, a result in the opposite direction would be interesting, too.) Both times, compute the 95% confidence interval of the sample mean as well

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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Textbook exercise:

A city’s status and living conditions may affect how its residents perceive their mayor and city council. Dr. Benevita has used data from Statistics Canada to rank larger metropolitan areas against each other. Focusing on unemployment rates, median household income, and crime rates, he has given Calgary an overall positive ranking (low unemployment, high income, and relatively low crime), and Winnipeg an overall negative one (mid-range unemployment, fairly low income, and very high crime).

Dr. Benevita has contacted 40 residents of each city to respond to one simple question: “How competent do you believe your municipal leaders are in governing your city?” Participants rated their municipal government on a scale of -3 (completely incompetent) to +3 (completely competent).

A perfectly normal distribution around the central, neutral, point would have a mean of 0 and a standard deviation of 1.66. We will use this as our comparison point to determine whether residents of Calgary and Winnipeg have an overall positive or negative view of their municipal government.

μ = 0.00, SD = 1.66
1. In Calgary, the 40 surveyed residents gave their municipal leaders a mean rating of 0.65. In Winnipeg, the 40 surveyed residents gave a mean rating of -1.18.
2. complete the 5 steps of Hypothesis Testing twice (once for each city) to answer the two research questions here:

Do residents of Calgary have an overall positive view of their municipal government?
Do residents of Winnipeg have an overall negative view of their municipal government?

In both cases, this will be a 2-tailed test with a .05 significance level. (Despite the fact that our research questions are both directional, a result in the opposite direction would be interesting, too.)

Both times, compute the 95% confidence interval of the sample mean as well

Determining the Characteristics of a Distribution of Means (for use in Step 2)
Rule 1. The mean of a distribution of means is the same as the mean of the population of
individuals.
μM = μ
Rule 2a. The variance of a distribution of means is the variance of the population of individuals
divided by the number of individuals in your sample.
o²M =
0²
n
Rule 2b. The standard deviation of a distribution of means is the square root of the variance of the
distribution of means.
OM= √O²M=
n
Rule 3. The shape of a distribution of means is approximately normal if either (a) each sample is of
30 or more individuals, or (b) the distribution of the population of individuals is normal.
The Five Steps of Hypothesis Testing with Means
Step 1. Define the populations, and restate the question as a research hypothesis and a null
hypothesis about those populations. (A directional research hypothesis is preferable, if logic leads
you to expect a particular direction; a non-directional null hypothesis will still be tested.)
Step 2. Determine the characteristics of the comparison distribution (the population norm).
Step 3. Determine the cutoff sample score on the comparison distribution at which the null
hypothesis should be rejected (i.e., determine the critical cutoff score(s) for z).
Step 4. Determine your sample's score on the comparison distribution.
Z=
M-μM
OM
Step 5. Decide whether to reject the null hypothesis.
Calculating the 95% Confidence Interval
95% CI = M (1.96)(OM)

Definition Definition Middle value of a data set. The median divides a data set into two halves, and it also called the 50th percentile. The median is much less affected by outliers and skewed data than the mean. If the number of elements in a dataset is odd, then the middlemost element of the data arranged in ascending or descending order is the median. If the number of elements in the dataset is even, the average of the two central elements of the arranged data is the median of the set. For example, if a dataset has five items—12, 13, 21, 27, 31—the median is the third item in ascending order, or 21. If a dataset has six items—12, 13, 21, 27, 31, 33—the median is the average of the third (21) and fourth (27) items. It is calculated as follows: (21 + 27) / 2 = 24.

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