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 17.8 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 = 1.88
B) t = 1.83
C) t = 1.75
D) t = 2.21

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: $t = \frac{17.8 - 16.9}{(2.4/\sqrt{25})} = \frac{0.9}{(2.4/5)} = \frac{0.9}{0.48} = 1.875$, which rounds to 1.88.

Given: Null Hypothesis Is That the Population Mean Is 16