Problem Description:
This Statistics Analysis Assignment Project revolves around a critical question: "How much do you spend on electronics daily?" With the rapid advancements in technology, people are increasingly drawn to the latest gadgets such as phones, computers, and sound systems. This demand has manufacturers continuously improving their products. To better understand this trend, the project focuses on the spending habits of employees at PWC, a significant player in the electronics market.
Solution
Introduction (5 points total)
Why you chose the project? (2 points)
The choice of this project is driven by the ever-evolving technology landscape. People's preference for cutting-edge electronics has grown, making it crucial to explore their spending habits.
What is your research question? (1 point)
The research question asks: "How much do you spend on electronics daily?"
What does the data represent? (1 point)
The data represents the daily spending on electronics by individuals, measured in USD ($).
What is your alpha and why? (1 point)
The alpha is set at 0.05, as it's a standard level of significance.
Sampling Procedure (5 points)
Describe your sampling method. (1 point)
A sample of 100 PWC employees was randomly chosen, and they were asked about their monthly spending on electronics. The daily average was derived by dividing the total by 30.
Who is the population? (1 point)
The population consists of all PWC employees.
Who is the sample? (1 point)
The sample comprises 100 individuals randomly selected for analysis.
What did you do to avoid bias? (1 point)
To prevent bias, a random number assignment and selection process were employed. The question posed to individuals was: "On average, how much money have you spent on electronics?"
Data (5 points)
(Data table not provided here)
Include graph(s) for the data. (3 points)
A graph (e.g., histogram) displays the data distribution.
Explanation of the graph(s). (2 points)
The graph illustrates that most respondents spend between $60 and $70 daily on electronics.
Hypothesis Test (35 points)
Write your null hypothesis (Ho) and alternative hypothesis (Ha) in symbols and complete sentences.
Ho: μ = $60
Ha: μ ≠ $60
Check the conditions. (3 points)
- Random Sample and Independence: The data was collected randomly.
- Normal: The sample size is larger than 25, allowing for the assumption of normality for a T-Test.
- Big Population: The PWC employee population exceeds 10 times the sample size (100), satisfying the condition.
Show your calculations worked out. (5 points)
μ = $60 Sample Mean (x̄) = 64.82 Standard Deviation (s) = 25.13 Sample Size (n) = 100
t = (64.82 - 60) / (25.13/√100) = 2.08
Conduct the test and label your test statistic and your p-value. (2 points)
Test Statistic: t = 2.08 P-value: p ≈ 0.0376
Include a graph for the hypothesis testing and explanation. (5 points)
Graph the p-value and compare it to the alpha (0.05). Since p ≈ 0.0376 < α, we REJECT HO.
Write the conclusion to your hypothesis testing in the context of the problem. (5 points)
We reject the null hypothesis (H0) because the p-value is less than the critical value (α). Consequently, we conclude that the amount spent on electronics by PWC employees is $60 on average, as initially hypothesized.
Complete a confidence interval and explain the results. (5 points)
Sample Size: 100 Sample Mean: 64.82 Standard Deviation: 25.13 Confidence Level: 95%
Confidence Interval: $59.89 to $69.3
We can be 95% confident that the average amount spent on electronics by PWC employees falls within the range of $59.89 and $69.3.
Paragraph reflection on what you learned from this project. (5 points)
Upon receiving the dataset from PWC, it was surprising to find that the average monthly spending on electronics by employees exceeded the national average of $60. This project has offered valuable insights into the spending habits of PWC employees, shedding light on the demand for the latest electronic gadgets.