Question

Bob has a bulb factory that produces two types of bulbs: white light (x) and color light (y). It is known that the standard deviation of service life for the population of white light bulbs is hours and hours for color bulbs, both are normally distributed. He tested the mean service life of those two types of bulbs by randomly drawing a sample of 20 bulbs from each type. The estimated mean service life are hours and hours. Assume that . What is the absolute value of the t-statistic if the null hypothesis is that both types of bulbs have the same service life?

Answer 1

The answer is "3.51".

Explanation:

`\to t=\frac{\bar{x}-\bar{y}}{\sqrt{(\sigma_x^2)/(n_x)+(\sigma_y^2)/(n_y)}}\\\\`

`=\frac{960-945}{\sqrt{(14^2)/(20)+(13^2)/(20)}}\\\\=\frac{15}{\sqrt{(196)/(20)+(169)/(20)}}\\\\=\frac{15}{\sqrt{(196+169)/(20)}}\\=\frac{15}{\sqrt{(365)/(20)}}\\\\=(15)/(√(18.25))\\\\=(15)/(4.27)\\\\=3.51`