Some Excel Calculations

Questions in this section require you to calculate the sample mean of all relevant values in a given sample with excel.  Please refer to the excel demo posted on canvas for assistance

1. To answer this question, you need to download the Excel file “Question1.xlsx” from Canvas (the page of “Assignment 2”).  This data set contains observations from a random sample of young economics graduates. For each individual in the sample, the height (in inches) and age are recorded.

What is the sample mean for 23-year-old economics graduates?

2. To answer this question, you need to download the Excel file “Question 2.xlsx” from Canvas. This data set contains data on emailing among employees in different divisions of a medium size company.

To better understand the amount of emailing, the company created a sample of employeeto- employee emailing activity. Each employee was asked to monitor the number of emails     he or she received from colleagues within 24 hours.

Consider two types of observations: (1) the number of e-mails received by any employee (regardless of division) within any 24-hour time period, and (2) the number of e-mails received by a Division F Employee within any 24-hour period. Which of the following is true

A.) During the 24 hours being tracked, the sample mean of the number of e-mails received by any employee is larger than the sample mean of the number of emails received by a Division F employee.

B.) During the 24 hours being tracked, the sample mean of the number of e-mails received by any employee is equal to the sample mean of the number of emails received by a Division F employee.

C.) During the 24 hours being tracked, the sample mean of the number of e-mails

received by any employee is smaller than the sample mean of the number of emails received by a Division F employee.

D.) None of the above

Normal Distribution

3. The probability distribution of customers that walk into a coffee shop on any given day of the week is described by a normal distribution with mean equal to 100 and standard deviation equal to 10

(a) What is the probability that between 100 and 120 customers walk into the coffee shop next Monday?

(b) What is the probability that at least 130 customers walk into the coffee shop next Monday?

(c) What is the probability that at most 110 customers walk into the coffee shop next Monday?

4. A major cell phone service provider has determined that the number of minutes per month that its customers use their phone is normally distributed with mean of 936.5 minutes with standard deviation of 44.25 minutes.  To reward customer loyalty, the company is thinking of providing a discount to customers who use the phone the most. In other words, if the number of minutes per month used by a customer is above a certain threshold, this customer will receive the discount. Calculate the threshold for the number of minutes used per month if the company only wishes to offer the rate discount to 2.5% of all customers.

Sampling

To answer Questions 5-6, you need to download the Excel file “Questions 5 and 6.xlsx from Canvas.

You also need Excel as a calculator in some steps. You will find the following Excel built-in functions helpful:  AVERAGE  (to calculate mean), STDEV  (to calculate standard deviation), SQRT to calculate square roots, and NORM .S .DIST (to calculate probabilities of the standard normal random variable Z

5. Jiang is interested in finding out how many blue chocolate beans a M&M fun-sized bag contains.  With the help of the two Econ 0150 sections she teaches, she has col- lected data from a sample of 88 bags. For each observation in the sample, the number of blue beans is recorded. The data is presented in the Excel file “Questions 3 and 4.xlsx”.

With a sample size of 88, how is the sample mean of the number of blue beans per bag distributed?

A.) It follows a normal distribution with mean = 3.25 blue beans and standard deviation = 1.74 blue bean.

B.) It follows a normal distribution with mean = 3.25 blue beans and standard deviation = 0.19 blue bean.

C.) It follows a non-normal distribution with mean = 3.25 blue beans and standard deviation = 1.74 blue bean.

D.) It follows a non-normal distribution with mean = 3.25 blue beans and standard deviation = 0.19 blue bean.

6. Based on the data in Question 5, calculate the probability that the average number of blue beans per bag for a sample of 88 M&M bags is more than 3.

To answer Questions 7-8, you need to download the Excel file “Questions 7 and 8.xlsx from Canvas

You also need Excel as a calculator in some steps. You will find the following Excel built-in functions helpful:  AVERAGE  (to calculate mean), STDEV  (to calculate standard deviation), SQRT to calculate square roots, and NORM .S .DIST (to calculate probabilities of the standard normal random variable Z.

Specifically, this data set contains the results of a survey on how much people are willing to pay for their favorite digital subscriptions in addition to their current payments. A sample of 48 people participated in the survey.  Their additional willingness to pay was measured in dollars.

7. Consider the group of people who are willing to spend at least $2 in addition to their current payments on their favorite digital subscriptions. With a sample size of 48, how is the sample proportion of this group of people distributed?

A.) It follows a normal distribution with mean = 0.521  (or 52.1%) and standard deviation = 0.072.

B.) It follows a non-normal distribution with mean = 0.521 (or 52.1%) and standard deviation = 0.072.

C.) It follows a normal distribution with mean = 0.521  (or 52.1%) and standard deviation = 0.505.

D.) It follows a non-normal distribution with mean = 0.521 (or 52.1%) and standard deviation = 0.505.

8. Based on the data in Question 7, what is the probability that in a sample of 48 people, the number of those who are willing to spend at least $2 on top of their current payments is between 24 and 30?

9. A study at a college on the west coast reveals that, historically, 36% of the students are minority students.  If a random sample of 100 students is selected, what is the probability that between 26.4% and 40.8% of students in the sample will be minority students?