Suppose the true proportion of voters in the county who support a specific candidate is 0.39 . Consider the distribution of sample statistics for the proportion of supporters with sample size 142. (a) What is the mean of this distribution (using a theory-based approach)? (b) What is the standard error of this distribution (using a theory-based approach)? Round to 2 places. (c) If we used the 2 standard deviation method to make our decision about whether or not the observed sample statistic was "usual/expected" vs. "unusual/unexpected," then what would be the low cutoff value and the high cutoff value for the observed statistic to be unusual? It would be unusual if the observed statistic was lower than It would be unusual if the observed statistic was higher than (d) Suppose the observed statistic is 0.47. Which conclusion would we make about the research question? The true proportion of voters in the county who support a restaurant tax is 0.39. It is plausible that the true proportion of voters in the county who support specific candidate is 0.39. We have statistically significant evidence that the true proportion of voters in the county who support a restaurant tax is not 0.39. The true proportion of voters in the county who support a restaurant tax is not 0.39.

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 the true proportion of voters in the county who support a specific candidate is 0.39

. Consider the distribution of sample statistics for the proportion of supporters with sample size 142.

(a) What is the mean of this distribution (using a theory-based approach)?

(b) What is the standard error of this distribution (using a theory-based approach)? Round to 2 places.

(c) If we used the 2 standard deviation method to make our decision about whether or not the observed sample statistic was "usual/expected" vs. "unusual/unexpected," then what would be the low cutoff value and the high cutoff value for the observed statistic to be unusual?
It would be unusual if the observed statistic was
lower than

It would be unusual if the observed statistic
was higher than

(d) Suppose the observed statistic is 0.47. Which conclusion would we make about the research question?

The true proportion of voters in the county who support a restaurant tax is 0.39.
It is plausible that the true proportion of voters in the county who support specific candidate is 0.39.
We have statistically significant evidence that the true proportion of voters in the county who support a restaurant tax is not 0.39.
The true proportion of voters in the county who support a restaurant tax is not 0.39.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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