For this project, we will be examining the lifespan of LED light bulbs sold by a hardware store named Schrute Farms. The store claims that these light bulbs have an average (mean) lifespan of 2600 hours. To verify this assertion, you decide to purchase twelve of these light bulbs and conduct a test on their lifespans. The recorded lifespans, in hours, are as follows:2551.3, 2623.4, 2489.7, 2672.5, 2607.8, 2584.1, 2701.6, 2523.8, 2634.9, 2680.7, 2598.4, 2547.2Initial Report:Before diving into the hypothesis testing questions, you are required to provide an initial report on the dataset. This report should include:Mean: Calculate the average lifespan of the light bulbs.Median: Identify the middle value in the ordered list of lifespans.Mode: Determine the most frequently occurring lifespan (if any).Five-number summary: Provide the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum.Range: Calculate the difference between the maximum and minimum lifespans.Interquartile Range (IQR): Determine the spread between the first and third quartiles.Standard Deviation: Compute the standard deviation of the sample.Variance: Calculate the variance of the sample.Boxplot: Create a boxplot to visually represent the distribution of the lifespans.Include these descriptive statistics and visualizations in your report to provide a thorough overview of the dataset.Question 1Assume that the population standard deviation is known and equal to 130 hours. At the 5% significance level, determine whether there is enough evidence to conclude that the mean lifespan is less than 2600 hours.Question 2Now, assume that the population standard deviation is unknown. At the 5% significance level, determine whether there is enough evidence to contradict the claim that the mean lifespan is 2600 hours.Project Tools (Suggested):You can use Google Docs for the report write-up and include your R findings. It is also suggested (not required) to use RStudio with R Markdown (.Rmd) or Quarto Markdown (.qmd) for statistical analysis and write-up. You can use R Markdown in RStudio to seamlessly integrate your R code with text explanations. This can be converted to a PDF.