In performing a hypothesis test where the null hypothesis is that the population mean is 4.8 against the alternative hypothesis that the population mean is not equal to 4.8, a random sample of 25 items is selected.The sample mean is 4.1 and the sample standard deviation is 1.4.It can be assumed that the population is normally distributed.The observed "t" value for this problem is _______.
A)-12.5
B)12.5
C)-2.5
D)-0.7
E)0.7

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: $t = \frac{4.1 - 4.8}{(1.4/\sqrt{25})} = \frac{-0.7}{(1.4/5)} = \frac{-0.7}{0.28} = -2.5$.

In Performing a Hypothesis Test Where the Null Hypothesis Is