Given: null hypothesis is that the population mean is 16.9 against the alternative hypothesis that the population mean is not equal to 16.9. A random sample of 25 items results in a sample mean of 18.0 and the sample standard deviation is 2.4. It can be assumed that the population is normally distributed. Determine the observed "t" value.
A) t = 2.29
B) t = 1.83
C) t = 1.75
D) t = 2.01

Question

Quizplus · Accepted Answer

The observed "t" value is calculated using the formula $t = \frac{\bar{x} - \mu}{(s/\sqrt{n})}$, where $\bar{x}$ is the sample mean, $\mu$ is the population mean, $s$ is the sample standard deviation, and $n$ is the sample size. Plugging in the given values: $t = \frac{18.0 - 16.9}{(2.4/\sqrt{25})} = \frac{1.1}{(2.4/5)} = \frac{1.1}{0.48} = 2.29$.

Given: Null Hypothesis Is That the Population Mean Is 16