Question

1)A rewiew of voted registration record in a small town yielded the dollowing data of the number of males and females registered as Democrat,

Modeling data distributions
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asked 2020-11-07

1)A rewiew of voted registration record in a small town yielded the dollowing data of the number of males and females registered as Democrat, Republican, or some other affilation:

\(\begin{array}{c} Gender \\ \hline Affilation & Male & Female \\ \hline Democrat & 300 & 600 \\ Republican & 500 & 300 \\ Other & 200 & 100 \\ \hline \end{array}\)

What proportion of all voters is male and registered as a Democrat? 2)A survey was conducted invocted involving 303 subject concerning their preferences with respect to the size of car thay would consider purchasing. The following table shows the count of the responses by gender of the respondents:

\(\begin{array}{c} Size\ of\ Car \\ \hline Gender & Small & Medium & lange & Total \\ \hline Female & 58 & 63 & 17 & 138 \\ Male & 79 & 61 & 25 & 165 \\ Total & 137 & 124 & 42 & 303 \\ \hline \end{array}\)

the data are to be summarized by constructing marginal distributions. In the marginal distributio for car size, the entry for mediums car is ?

Answers (1)

2020-11-08

1) Given data table , \(\begin{array}{|c|c|} \hline Gender \\ \hline Affiliation & Male & Female & Total \\ \hline Democrat & 300 & 600 & 900 \\ \hline Republican & 500 & 300 & 800 \\ \hline Other & 200 & 100 & 300 \\\hline Total & 1000 & 1000 & 2000 \\ \hline \end{array}\) Number of all voters male and registered as a democrat x = 300 Total voters = n = 2000 Proportion of all voters is male and registered as democrat is , \(\frac{x}{n} = \frac{300}{2000} = 0.15\)

2) Given data table, \(\begin{array}{c} Size\ of\ Car \\ \hline Gender & Small & Medium & lange & Total \\ \hline Female & 58 & 63 & 17 & 138 \\ Male & 79 & 61 & 25 & 165 \\ Total & 137 & 124 & 42 & 303 \\ \hline \end{array}\) The marginal distribution of car size, \(\begin{array}{|c|c|} \hline Size\ of\ car & small & medium & large & total \\ \hline Probability & \frac{137}{303} = 0.452 & \frac{124}{303} = 0.409 & \frac{42}{303} = 0.137 & 1\\ \hline \end{array}\) In the marginal distribution for car size, the entry for medium cars is 0.409

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Because the interval contains both positive and negative numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is greater than that of Denver.
Because the interval contains only negative numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is less than that of Denver.

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