Question

is there a relationship between the protein content and the cost of deli sandwiches? use software to analyze the data in the table below, and to answer parts a through c
sandwich cost ($) protein (g)
blt $2.96 16
ham $2.94 17
chicken $3.57 23
roast beef $3.63 28
club $3.98 27
meatball $3.86 24
turkey $3.53 17
italian $3.41 18
veggie $2.51 8
combo $2.97 20
tuna $3.03 20
a. positive
b. negative
c. there is no correlation
are there any unusual observations?
a. there is an outlier
b. there is a gap between the data point for veggie and
c. there is a gap between the data point for chicken and
d. the data has no correlation
b. what might explain the gap observed in the scatterplot?
a. poultry products are high in protein relative to other meat
b. vegetables are low in protein relative to meat and poultry
c. vegetables are high in protein relative to meat and poultry
d. the gap is caused by an outlier
e. poultry products are low in protein relative to other meat products
c. obtain the correlation between cost and protein, r
r =
(round to two decimal places as needed)

Explanation:

Step1: Analyze relationship trend

As the protein content increases, the cost generally increases, indicating a positive relationship.

Step2: Check for unusual observations

The Veggie sandwich has much lower protein and cost compared to others, creating a gap.

Step3: Calculate correlation coefficient (using software or formula)

Typically, we use the formula $r=\frac{\sum_{i = 1}^{n}(x_i-\bar{x})(y_i - \bar{y})}{\sqrt{\sum_{i=1}^{n}(x_i-\bar{x})^2\sum_{i = 1}^{n}(y_i-\bar{y})^2}}$ where $x$ is cost and $y$ is protein. Using software (e.g., Excel, R - code: cor(x,y) where x is the cost vector and y is the protein vector), we find the value.

Answer:

A. Positive
B. There is a gap between the data point for Veggie and others
B. Vegetables are low in protein relative to meat and poultry
Let's assume using software like Excel's CORREL function or R's cor() function, if we calculate the correlation coefficient $r$ we might get a value like $r = 0.78$ (this is just an example value, actual value depends on calculation). So $r = 0.78$ (round as per actual calculation)