Question

for the following two - way tables, complete the tables and answer the questions.
31 a total of 500 people were surveyed regarding their grocery shopping preferences, whether they prefer in - person shopping or pick - up/delivery, and if they prefer regular checkout or self - checkout. complete the table of the results, and then use the results to answer the following questions

	in - person shopping	pick - up/delivery	total
self checkout
total		175

a what percentage of people prefer shopping in - person and using self - checkout?
b how many people prefer regular checkout and pick - up/delivery?
c of those who prefer regular checkout, what is the relative frequency of those who prefer in - person shopping?
d how many more people prefer self - checkout over regular checkout?
32 twenty freshmen and twenty sophomores were surveyed about their pets. thirteen sophomores said they had dogs. out of the 20 freshmen, 9 had cats. fill out the two - way table below, then answer the following questions.

	freshmen	sophomores	total
cats
total

a how many sophomores have cats?
b how many students own dogs?
c how many freshmen have dogs?
d what percentage of students own cats?
e what percentage of students surveyed were freshmen?
f what is the relative frequency of freshmen dog owners?
g out of the sophomores, what is the relative frequency of owning a cat?
h is there an association between grade levels and pet choice?

Explanation:

Problem 31

Step1: Complete the two-way table

First, total surveyed = 500.

• Total pick up/delivery = 175, so total in-person = $500 - 175 = 325$
• Regular checkout total: $180$ (given total regular), so self checkout total = $500 - 180 = 320$
• In-person self checkout = $325 - 80 = 245$
• Pick up/delivery regular checkout = $180 - 80 = 100$
• Pick up/delivery self checkout = $175 - 100 = 75$

Final table:

	IN-PERSON SHOPPING	PICK UP/DELIVERY	TOTAL
SELF CHECKOUT	245	75	320
TOTAL	325	175	500

Step2: Solve part (a)

Find % of in-person + self checkout:
$\text{Percentage} = \frac{245}{500} \times 100\% = 49\%$

Step3: Solve part (b)

From table, regular + pick up/delivery = 100

Step4: Solve part (c)

Relative frequency (in-person regular / total regular):
$\text{Relative Frequency} = \frac{80}{180} = \frac{4}{9} \approx 0.444$

Step5: Solve part (d)

Difference: $320 - 180 = 140$

Step1: Complete the two-way table

Total freshmen = 20, total sophomores = 20, total surveyed = 40.

• Freshmen with cats = 9, so freshmen with dogs = $20 - 9 = 11$
• Sophomores with dogs = 13, so sophomores with cats = $20 - 13 = 7$
• Total dog owners = $11 + 13 = 24$
• Total cat owners = $9 + 7 = 16$

Final table:

	FRESHMEN	SOPHOMORES	TOTAL
CATS	9	7	16
TOTAL	20	20	40

Step2: Solve part (a)

Sophomores with cats = 7

Step3: Solve part (b)

Total dog owners = 24

Step4: Solve part (c)

Freshmen with dogs = 11

Step5: Solve part (d)

% of cat owners: $\frac{16}{40} \times 100\% = 40\%$

Step6: Solve part (e)

% of freshmen: $\frac{20}{40} \times 100\% = 50\%$

Step7: Solve part (f)

Relative frequency (freshmen dogs / total dog owners):
$\frac{11}{24} \approx 0.458$

Step8: Solve part (g)

Relative frequency (sophomore cats / total sophomores):
$\frac{7}{20} = 0.35$

Step9: Solve part (h)

Compare pet preference rates:

• Freshmen cat rate: $\frac{9}{20}=45\%$, dog rate: $\frac{11}{20}=55\%$
• Sophomore cat rate: $\frac{7}{20}=35\%$, dog rate: $\frac{13}{20}=65\%$

Sophomores are more likely to own dogs, freshmen more likely to own cats, so yes, there is an association.

Answer:

a. $49\%$
b. $100$
c. $\frac{4}{9}$ (or ~44.4%)
d. $140$

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Problem 32