Reference no: EM134045503

Introductory Statistics

Assessment

Island Brew Café is a small coffee shop located in Castries. The café sells coffee, tea, smoothies, pastries, and sandwiches. The owner wants to use statistics to better understand the café's customers, sales, and daily operations.

The owner has collected information from a sample of customers and from the café's daily records. You have been asked to analyze the information and provide statistical results that can assist the owner in understanding the business.

Question 1

The owner of Island Brew Café has determined that the café's average monthly revenue over the past five years was EC$18,500. She randomly selected 12 months from the past year and found that the average monthly revenue for these 12 months was EC$20,350.

Does the value EC$18,500 refer to a parameter or a statistic?

Is the value EC$20,350 a parameter or a statistic?

State two advantages of using a sample statistic rather than collecting information from the entire population.

For each the following variables, state which is quantitative and which is qualitative. If it is quantitative, state whether it is discrete or continuous.

The amount of milk, in millilitres, used to prepare a customer's drink.

The number of customers served by the café in one day.

The type of drink ordered by a customer.

Question 2

Island Brew Café has 80 regular customers divided into four customer categories:

Customer Category  Number of Customers
Students  20
Teachers  25
Office Workers  15
Other Customers  20
Total  80

The owner wants to select a sample of 20 customers to determine their average monthly spending at the café.

Identify the sampling techniques suggested by each of the methods A, B, C and D

The owner writes the name of every regular customer on a separate piece of paper, places all the papers in a box, mixes them, and randomly selects 20 names.

The owner selects customers so that the sample contains students, teachers, office workers, and other customers in the same proportions as they appear in the population.

The owner obtains an alphabetical list of the 80 regular customers and selects every 4th customer until 20 customers have been selected.

The owner selects customers until she has 5 students, 6 teachers, 4 office workers, and 5 other customers.

Question 3

The café recorded the number of customers served per month. The data are presented in the following stem-and-leaf display.

Stem-and-Leaf Display
N = n   Leaf Unit = 100.0

3   2   233
8   3   23556
(z)   4   00677779
y   5   234556
3   6   78
1   7   7

Determine the value of z and y.

What was the sample size, n?

Determine the following
Mode [1]
Median [1]
Range [2]

The table below shows the sugar content in 20 cups of coffee

Weight    Frequency
6-10    4
11-15    6
16-20    7
21-25    3

Using the table above to calculate the sample mean of the dataset.

the mode of the dataset.

the sample variance of the dataset.

Question 4

Island Brew Café surveyed 100 customers about the type of drink they usually purchase. The results are shown below.

    Coffee    Tea    Matcha    Total
Students    25    15    10    50
Non-Students    20    20    10    50
Total    45    35    20    100

One customer is selected at random from the 100 customers surveyed.

Find the probability that a student purchased a coffee.

Find the probability that the selected customer was a student or purchased a matcha.

Given that the customer was a non-student, what is the probability that he/she purchased tea.