Assume That a Simple Random Sample Has Been Selected from a Normally

question 1

Essay

Assume that a simple random sample has been selected from a normally distributed population. Find the test statistic, P-value, critical value(s), and state the final conclusion.
-In tests of a computer component, it is found that the mean time between failures is 520 hours. A modification is made which is supposed to increase the time between failures. Tests on a random sample of 10 modified components resulted in the following times (in hours)between failures. $$\begin{array} { l l l l l } 518 & 548 & 561 & 523 & 536 \\499 & 538 & 557 & 528 & 563\end{array}$$ At the 0.05 significance level, test the claim that for the modified components, the mean time between failures is greater than 520 hours.

---

Definitions:

Sensitivity

The quality of being responsive or susceptible to environmental changes or to the feelings of others; a capacity for noticing and responding to stimuli or emotional cues.

Hering-Helmholtz Illusion

An optical illusion related to depth perception, where a flat image appears to be three-dimensional due to specific visual cues.

Visual Illusion

A misinterpretation of a real external stimulus, where what we perceive does not correspond to the physical reality of the world around us.

Active Touching

The deliberate use of touch by individuals to explore objects and environments, enhancing sensory and perceptual experiences.