Question

a national survey asked people, \how often do you eat out for dinner, instead of at home?\ the frequencies were as follows. complete parts (a) through (g).

\

$$\begin{tabular}{|l|c|} \\hline response & frequency \\\\ \\hline never & 212 \\\\ rarely & 543 \\\\ sometimes & 936 \\\\ most of the time & 392 \\\\ always & 42 \\\\ \\hline \\end{tabular}$$

(f) construct a pie chart. choose the correct answer below.

(g) suppose a person claims that, \2.0\\% of all people in the nation always eat out.\ is this a descriptive or inferential statement?

Explanation:

⚡ Using what you learned: displaying data: bar graphs & circle graphs · 🆕 New Concept: Descriptive vs. Inferential Statistics
Generalizing sample data to a larger population

Step 1: Calculate the total frequency and relative percentages

To determine the correct pie chart, we first find the total number of survey respondents:

$$ \text{Total} = 212 + 543 + 936 + 392 + 42 = 2125 $$

Next, we calculate the relative percentage for each response category:

• Never (N - Blue):

$$ \frac{212}{2125} \approx 10.0\% $$

• Rarely (R - Red):

$$ \frac{543}{2125} \approx 25.6\% $$

• Sometimes (S - Green):

$$ \frac{936}{2125} \approx 44.0\% $$

• Most of the time (M - Yellow):

$$ \frac{392}{2125} \approx 18.4\% $$

• Always (A - Purple):

$$ \frac{42}{2125} \approx 2.0\% $$

Step 2: Identify the correct pie chart

We look for the pie chart that matches these proportions:

• Sometimes (Green): Almost half of the circle (\(44\%\)).
• Rarely (Red): Just over a quarter of the circle (\(25.6\%\)).
• Most of the time (Yellow): About \(18.4\%\).
• Never (Blue): Exactly \(10\%\).
• Always (Purple): A very small sliver (\(2\%\)).

Comparing the options:

• In A and B, the "Always" (Purple) slice is missing or colored incorrectly (yellow is used instead of purple for the smallest slice).
• In C and D, the purple slice represents "Always" (\(2\%\)) and the yellow slice represents "Most of the time" (\(18.4\%\)).
• Comparing C and D, we look at the blue slice ("Never" = \(10\%\)) and the purple slice ("Always" = \(2\%\)). In C, the blue slice is noticeably larger than the purple slice, representing the \(10\%\) to \(2\%\) ratio correctly. In D, the blue and purple slices are nearly identical in size, which is incorrect.

Thus, C is the correct pie chart.

Step 3: Determine if the statement in (g) is descriptive or inferential

The statement is: "2.0% of all people in the nation always eat out."

• Descriptive statistics only describe the actual data collected from the sample (e.g., "2.0% of the surveyed people always eat out").
• Inferential statistics take a result from a sample and extend/generalize it to make a claim about the entire population ("all people in the nation").

Because this statement makes a claim about the entire national population based on a sample survey, it is an inferential statement.

Answer:

(f) C
(g) inferential