$.$ LED light bulbs are renowned for their longevity, outlasting incandescent, halogen,

and fluorescent bulbs. Typically, an LED bulb can last over $5$ years. These bulbs are

not only energy$-$efficient but also come in various styles, shades, and shapes.

Powergen Italia, an Italian company that manufactures LED light bulbs asserts that

their long$-$life bulb can last, on average, more than $50,000$ hours. A statistician

decided to test this claim. He selected a random sample of $100$ bulbs from the

manufacturer and recorded the time until each bulb stopped working. Based on this

sample, can we confidently assert, with a $5\%$ level of significance, that the manufacturer$$s

claim about the average lifespan of their bulbs is accurate? The data for this test is located in the

Bulbs tab of the Excel file Week $13$ ASMT Data.xlsx Excel file.