STAT 1100 Spring 2024

STAT 1100 Spring 2024

Excel Lab 2

In this statistics lab, students will utilize Excel to conduct hypothesis tests, applying the concepts learned in the classroom to real-world scenarios. The Lab focuses on getting insight into population parameters such as average spending, starting salaries, or commute times, using appropriate statistical tests. Students will analyze data sets related to these scenarios and perform hypothesis tests, including one-sample t- tests, two-sample t-tests, and chi-squared tests for independence, to draw conclusions and make informed decisions based on statistical evidence. Through hands-on practice with Excel, students will enhance their understanding of hypothesis testing methodologies and gain valuable skills in data analysis and interpretation.

Note: Each data set is contained in one sheet of the “Lab2_Data.xlsx” Excel file. For example, exercise 1 data is contained in the “Exercise_ 1” sheet.

Note: Assume that the significance level for the tests is fixed at 0.05.

Exercise 1. A market research firm conducted a survey to investigate the proportion of Apple iPhone users who own an Apple  Watch, with a sample size of 1000 iPhone users surveyed. Among the respondents, 774 reported owning an Apple Watch. The firm hypothesized that 80% of iPhone users own an Apple Watch.

a)   Run a hypothesis test to see if the proportion of all iPhone users deviates from Apple’sconjecture.

b)  Create a 95% CI for the proportion of iPhone users that own an Apple Watch.

Exercise 2.A telecommunications company is analyzing the trend in the average number of subscriptions per user over the past five years. From a sample of 100 users, they found that the average number of subscriptions per user is 2.91, with a known population standard deviation of 1. They hypothesize that the average number of subscriptions per user was 2 in the past. Use a hypothesis test to determine if there has been an increase in the average number of subscriptions per user in the last five years.

Exercise 3. The city of Pittsburgh has implemented a new traffic congestion reduction plan aimed at improving commute times for residents and reducing traffic-related stress. The plan involves various measures such as optimizing traffic signal timings, implementing carpool lanes, and promoting public transportation. City officials want to assess the effectiveness of the plan in reducing average commute times for residents. Before the implementation of the congestion reduction plan, the mean commute time for a Pittsburgher was 45 minutes. Data was collected from a sample of 200 commuters who regularly travel during peak hours in Pittsburgh. Run a test to determine if the mean commute time for Pittsburgh’s citizens has decreased in the last 5 years ago.

Exercise 4.A group of researchers at the University of Pittsburgh (Pitt) aims to investigate whether there is a significant difference in the average spending of Pitt students at two popular fast-food restaurants, Chick-Fil-A and Raising Cane's. They collect spending data from a random sample of 117 Pitt students and record each student's spending at Chick-Fil-A and Raising Cane's. Run a paired t-test for testing the hypothesis that students spend about the same amount on either of the restaurants.

Exercise 5. A comparative study is conducted to assess the difference in the average starting salaries of business graduates from the Katz Graduate School of Business at the University of Pittsburgh (Pitt) and the Smeal College of Business at Penn State University (Penn State). Data on the starting salaries of a random sample of 52 business graduates from each institution is collected separately. Run a two-sample hypothesis test to determine if the average starting salaries for Penn State graduates are higher than for Pitt alumni. You can assume equal variances for the two groups.

Exercise 6. At a superhero convention, organizers decide to conduct a survey to understand the pizza preferences of attendees based on their favorite superhero. They suspect that there might be a relationship between a person's favorite superhero and their pizza topping choices. They gathered information from 265 attendees, here is the table of results.

Run a test to see if the preferred pizza toppings are related to the attendees’ favorite superhero.