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.

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Definitions:

Assumption of Normality

The presumption that the data in a dataset is normally distributed, which is a common precondition for many statistical tests.

Descriptive Statistics

Statistical methods that describe and summarize data through measures such as mean, median, mode, and standard deviation.

Variables

Variables are symbols or names that represent values or characteristics that can vary within a study or experiment.

Evaluate Scores

The process of analyzing and assessing the scores obtained in a test or assessment.