11. the snoqualmie are native americans living in western washington state, near a spectacular 268-foot waterfall. anthropologists recently studied the religious significance of the falls to two groups of contemporary snoqualmie: those living in the traditional valley (within 25 miles of the falls) and those living in the surrounding region. from responses to a survey, the researchers categorized individual levels of perceived religious significance as low, medium, and high. their results are shown in the table and graph.

table and graph omitted here, table has encounter level (low, medium, high, total) and location of residence (surrounding region, traditional valley, total) with numbers: low: 25, 17, 42; medium: 8, 21, 29; high: 5, 12, 17; total: 38, 50, 88. graph is a segmented bar graph with surrounding region and traditional valley, showing low, medium, high relative frequencies.

a. which variable is the explanatory variable? explain.

b. what proportion of the total sample are living in the traditional valley?

c. what proportion of those living in the surrounding region report a medium level of religious experience?

d. what proportion of those living in the traditional valley report a medium level of religious experience?

e. is there an association between the location of residence and encounter level? explain.

f. how would a mosaic plot look different than the segmented bar graphs presented?

Question

11. the snoqualmie are native americans living in western washington state, near a spectacular 268-foot waterfall. anthropologists recently studied the religious significance of the falls to two groups of contemporary snoqualmie: those living in the traditional valley (within 25 miles of the falls) and those living in the surrounding region. from responses to a survey, the researchers categorized individual levels of perceived religious significance as low, medium, and high. their results are shown in the table and graph.

table and graph omitted here, table has encounter level (low, medium, high, total) and location of residence (surrounding region, traditional valley, total) with numbers: low: 25, 17, 42; medium: 8, 21, 29; high: 5, 12, 17; total: 38, 50, 88. graph is a segmented bar graph with surrounding region and traditional valley, showing low, medium, high relative frequencies.

a. which variable is the explanatory variable? explain.

b. what proportion of the total sample are living in the traditional valley?

c. what proportion of those living in the surrounding region report a medium level of religious experience?

d. what proportion of those living in the traditional valley report a medium level of religious experience?

e. is there an association between the location of residence and encounter level? explain.

f. how would a mosaic plot look different than the segmented bar graphs presented?

Accepted Answer

### Part a
# Brief Explanations:
The explanatory variable is the one that is thought to explain or predict changes in another variable. Here, the location of residence (traditional valley or surrounding region) is used to explain the perceived religious significance (encounter level). So the explanatory variable is location of residence because we are studying how residence location might affect religious significance levels.
# Answer:
The explanatory variable is the location of residence (traditional valley or surrounding region). This is because we are investigating how the location of where the Snoqualmie live (residence location) might explain or influence their perceived religious significance (encounter level).

### Part b
# Explanation:
## Step1: Identify total sample and traditional valley count
The total sample size (from the "Total" row and "Total" column) is 88. The number of people living in the traditional valley (from the "Total" row and "Traditional valley" column) is 50.
## Step2: Calculate the proportion
The proportion is calculated as the number of people in the traditional valley divided by the total sample size. So the proportion is $\frac{50}{88}$. Simplifying this fraction (or converting to a decimal), we get approximately 0.5682 or 56.82%.
# Answer:
The proportion of the total sample living in the traditional valley is $\frac{50}{88}\approx0.568$ (or 56.8%).

### Part c
# Explanation:
## Step1: Identify surrounding region total and medium count
The total number of people living in the surrounding region (from the "Total" row and "Surrounding region" column) is 38. The number of people in the surrounding region with a medium level of religious experience (from the "Medium" row and "Surrounding region" column) is 8.
## Step2: Calculate the proportion
The proportion is the number of medium - level responses in the surrounding region divided by the total number of people in the surrounding region. So the proportion is $\frac{8}{38}\approx0.2105$ or 21.05%.
# Answer:
The proportion of those living in the surrounding region who report a medium level of religious experience is $\frac{8}{38}\approx0.211$ (or 21.1%).

### Part d
# Explanation:
## Step1: Identify traditional valley total and medium count
The total number of people living in the traditional valley (from the "Total" row and "Traditional valley" column) is 50. The number of people in the traditional valley with a medium level of religious experience (from the "Medium" row and "Traditional valley" column) is 21.
## Step2: Calculate the proportion
The proportion is the number of medium - level responses in the traditional valley divided by the total number of people in the traditional valley. So the proportion is $\frac{21}{50} = 0.42$ or 42%.
# Answer:
The proportion of those living in the traditional valley who report a medium level of religious experience is $\frac{21}{50}=0.42$ (or 42%).

### Part e
# Brief Explanations:
To determine if there is an association, we compare the proportions of each encounter level across the two residence locations. For low level: in surrounding region, proportion is $\frac{25}{38}\approx0.658$, in traditional valley, $\frac{17}{50} = 0.34$. For medium level: surrounding region $\frac{8}{38}\approx0.211$, traditional valley $\frac{21}{50}=0.42$. For high level: surrounding region $\frac{5}{38}\approx0.132$, traditional valley $\frac{12}{50}=0.24$. Since the proportions of each encounter level differ between the two residence locations, there is an association between location of residence and encounter level.
# Answer:
Yes, there is an association. The proportions of each encounter level (low, medium, high) are different for those living in the surrounding region and those living in the traditional valley. For example, the proportion of low - level religious significance is higher in the surrounding region ($\approx0.658$) than in the traditional valley ($0.34$), while the proportion of medium - level is higher in the traditional valley ($0.42$) than in the surrounding region ($\approx0.211$), and the proportion of high - level is higher in the traditional valley ($0.24$) than in the surrounding region ($\approx0.132$). These differing proportions indicate an association between location of residence and encounter level.

### Part f
# Brief Explanations:
In a segmented bar graph, the bars for each group (surrounding region and traditional valley) have the same height (100% or the total count for each group). In a mosaic plot, the width of each bar is proportional to the size of the group (so the bar for the traditional valley, with 50 people, would be wider than the bar for the surrounding region, with 38 people), and the height of each segment within the bar is proportional to the proportion of the encounter level within that group. So the main difference is that the width of the bars in a mosaic plot is proportional to the sample size of each residence location group, while in the segmented bar graph, the bar heights are standardized (e.g., to 100% or to the total count of each group) and the widths are the same.
# Answer:
In a segmented bar graph, the bars for the surrounding region and traditional valley have the same width (or height is standardized, e.g., to 100% of the group's count). In a mosaic plot, the width of each bar (representing a residence location) is proportional to the size of the group (so the bar for the traditional valley, with 50 people, is wider than the bar for the surrounding region, with 38 people). The height of each segment within a bar in a mosaic plot is proportional to the proportion of the encounter level within that group, similar to the segmented bar graph, but the width variation based on group size is the key difference.

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QUESTION IMAGE

Question

Explanation:

Part a

Step1: Identify total sample and traditional valley count

Step2: Calculate the proportion

Step1: Identify surrounding region total and medium count

Step2: Calculate the proportion

Answer:

Part b